VECTOR ANALYSIS(B.Sc.Maths Notes)
88 videos • 1,270 views • by Doctor of Mathematics
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1.Scalar,Vector,Representation,Addition,Substraction of vectors;Triangular and Parallelogram law,Dis
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2-Distribution Law for vectors:Vecor Analysis
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Find the work done by the force F=(x^2-y^3)i+(x+y)j in moving a particle along the closed path C con
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Find the divergence of r unit vector. or div.r cap =2/r
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Show that the vector (siny+z,xcosy-z,x-y)irrotational
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Prove that : div.[rgradr^(-4)]=3r^(-4) or div.[r grad r^-3]=3r^-4
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Check for the linear dependence of the following system of vectors:u=(1,-1,1),v=(2,1,1),w=(3,0,2).if
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Let f(x,y,z)=x^3+y^3+z^3-3xyz;a point at which the gradient of the function f is equal to zero is:
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Calculate the gradient of 1/|r| Top mathematics channel on YouTube
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Prove that torque=r×f
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Find the area of circle of radius 'a' using Green's theorem.||Best Mathematics Channel on YouTube||
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grad(a.b)=ax curl b+bx curl a+(a.del)b +(b.del)a
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div.(a+b)=div.a+div.b
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Del x(fxr) =2f-(del.f) r+(r.del) f
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If a is a constant vector, then prove that del(a.u) =(a.del)u +axcurl u
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del. (axu) =-a.curl u
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Explanation of Shab-e-miraj and Isra on basis on special theory of relativity
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verify stokes'theorem for A=(y-z+2)I+(y-z+4)j -xzk,S is surface of cube x=0,y =0,z=0,x =2,y=2,z=2
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Find the unit vector normal to the surface x2.y+2xz=4 at the point (2,-2,3).
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a. {grad(u.a)-curl(uxa)}=a^2(div.u)
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Non-Collinear Vectors
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Position Vector
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Coplanar and non-coplanar Vectors
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If u=x+y+z, v=x^2+y^2+z^2, w=yz+zx+xy, then show that gradu, gradv and gradw are coplanar vectors.
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Show that del.{f(r)r/r}=1/r^2d/dr{r^2.f(r)}
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If n, a, b are constant and r=(cos nt)a+(sin nt)b prove r x dr/dt=na xb and d^2r/dt^2+n^2.r=0 vector
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div.grad(r^n)
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To express vector AB in terms of position vectors of its end point.
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Localized vector and Unlocalized Vector ||TOP MATHEMATICS CHANNEL ON YOUTUBE
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Find the work done in moving a particle once around circle C in xy-plane where C is given by x^2+y^2
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Prove that curl(uxv)=(v.del)u-(u.del)v+u div. v-v div. u
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Evaluate : d/dt(r.dr/dtxd^2r/dt^2) all vectors. ||Best Mathematics Channel on YouTube||Top Channel||
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To prove curl(AxB)=
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Prove that: ix(axi)+jx(axj)+kx(axk) =2a (All vectors)
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Evaluate d^2/dt^2[a da/dt d^2a/dt^2]
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Prove that: (axb)x(cxd)+(axc)x(dxb)+(axd)x(bxc) =2[b d c]a ||Top B Sc.Mathematics on YouTube free
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Show that ∫(axi+byj+czk).ndS=4π/3(a+b+c)
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If f=x^2zi-2y^3z^2j+xy^2zk, find curl f at point (1,-1,1).
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For Iradication of confusion in (A+B)X(A-B)=2BXA
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40
The equation of given circle is x^2+y^2=1.Why is not come out unit vector gradient of equation k?
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Evaluate: ∇^2(1/r) del^2(1/r) or div.(grad1/r)
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Find curl V,where V=e^xyz(i+j+k)
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Prove: div.r=3. or ∇.r=3
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r=acos(wt)i+bsin(wt)j (b)The force acting on the particle is always directed toward the origin
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यदि r=ae^nt+be^nt जहां a तथा b सदिश स्थिरांक हैं तब सिद्ध करो कि d^2r/dt^2-n^2r=0.
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If da/dt=rxa,db/dt=rxb,then prove that d(axb)/dt=rx(axb)
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If u=sinθi+cosθj+θk,v=cosθ i-sinθj-3,w=2i+3j-k,find d/dθ[ux(vxw) at θ=0
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वक्र r=4ti+t^2j+2t^3k के बिंदुओं t=1तथा t=2 पर स्पर्श रेखाओं के बीच का कोण ज्ञात करो.
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Show that :∫x^c/c^xdx=c+1/l(ogc)^c+1
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Prove that gamma n/c^n=∫e^-cy.y^n-1dy
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If m and n are positive real numbers,prove that ∫x^m-1(log1/x)^n-1dx.
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वक्र r=t^2i+2tj-t^3 k के बिंदुओं t=1तथा t=-1 पर खींची गई स्पर्श रेखाओं के बीच का कोण ज्ञात कीजिए
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एक कण वक्र x=2तथा के अनुदेश गतिशील है तो सदिश केअनुदिश वेग तथा त्वरण के वियोजित भाग ज्ञात करें जबकि
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यदि r=।r। और r=xi+yj+zk then find del r=r/r
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यदि r=t^3i+(2t^3-1/5t^2)j तो दर्शाइए कि rxdr/dt=k (vector)
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Find the divergence of r/r
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Show that rxdr=rxdr/r^2, where r=।r। (vectors)
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Define Scalar Triple Product.Give it's geometrical interpretation.
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If d^2r/dt^2=r, then show that rxdr/dt is a constant vector.r is vector.
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r=xi+yj+zk, find ∇r^n or Prove that ∇r^n.Find gradient of r^n. Find grad r^n.
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If r=acosωt+bsinωt, show that rxdr/dt=ω(axb) and d^2r/dt^2=-ω^2r (r,a,b are all vectors)
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Evaluate |dr/dt X d^2r/dt^2| and[dr/dt d^2r/dt^2 d^3r/dt^3],where r=(asint)i+(acost)j+(attanθ)k.
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63
Show that the four points whose position vectors are α,β,r,δ are coplanar if and only if [α β r]=[β
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If the directional derivative of the function f(x,y,z)=a(x+y)+b(y+z)+c(z+x) has maximum value 12 at
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Prove that|axb|²|axc|²-{(axb).(axc)}²=|a|²[a b c]².
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A particle acted on by constant forces 4i+j-3k and 3i+j-k is displayed from the point i+2j+3k to the
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[axb cxd exf]=[a b d][c e f]-[a b c][d e f]=[a b e][f c d]-[a b f][e c d]=[c d a][b e f]-[c d b][a ]
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Show that directional derivative of f=x²y²z² from point (2,1,-1) is maximum in direction 4i+8j-8k
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Prove that:[axb bxc cxa]=[a b c]²
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Prove that:ax(bxc)=(a.c)b-(a.b)c. [Vector triple product]
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If r=ae^nt+be^-nt;where a and b are constant vectors,show that d²r/d²t-n²r=0.
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Find the directional derivative for the function Φ=3xy+4yz+6xyz at the point (1,2,3) in the directio
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Evaluate the integral ∫F.dr where F=(siny)i+x(1+cosy)j and the curve C is the circular path given by
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Prove that Div.[r×(a×r)]=-2(r.a) ;where r=(x,y,z) and a is a constant vector.
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Scalar Function (Definition) vector calculus, Vector Analysis
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Geometrical Interpretation of the Vector Derivative
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Difference between vector and constant vector
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Difference between vector and constant vector
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If r=xi+yj+zk then curl r is equal to zero vector.
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Evaluate |dr/dt X d^2r/dt^2| and[dr/dt d^2r/dt^2 d^3r/dt^3],where r=(acost)i+(asint)j+(attanθ)k.
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Compute integral ydx+zdy+xdz over the twisted cubic curve defined by r=(t,t^2,t^3) from t=0 to t=1.
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Evaluate integral F.dr where F=zi+xyj-y^2k along the curve C:r(t)=t^2i+tj+√tk and t:0→1.
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Evaluate d^2/dx^2[r dr/dt d^2r/dt^2]
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The necessary and sufficient condition for the vector a(t) to have constant direction is axda/dt=0
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If r be a unit vector,then shiw that |rxdr/dt|=|dr/dt|
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If r be a unit vector, then show that |rxdr/dt|=|dr/dt|
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Evaluate Grad e^r^2 or Grad e^(x^2+y^2+z^2)
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If rxdr=0 , prove that r (cap)=constant vector
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