01:58

Find the angle between the vectors.𝑎=3𝑖−8𝑗+𝑘, 𝑏=4𝑖−𝑘

02:27

Determine whether the given vectors are orthogonal, parallel, or neither.

02:28

Determine whether the given vectors are orthogonal, parallel, or neither.

01:58

Find the angle between the vectors.𝑎=⟨1, −4, 1⟩, 𝑏=⟨0, 5, −5⟩

01:57

Find the angle between the vectors.𝑎=⟨1, −4, 1⟩, 𝑏=⟨0, 2, −2⟩

01:58

Find the angle between the vectors. 𝑎=⟨−7, 8⟩, 𝑏=⟨3, 4⟩

01:58

Find the angle between the vectors.𝑎=⟨−3, 7⟩, 𝑏=⟨3, 4⟩

01:58

Find the angle between the vectors. 𝑢=⟨7, 4⟩, 𝑣=⟨6, 1⟩

01:57

Find the angle between the vectors. 𝑎=⟨7, 4⟩, 𝑏=⟨2, −1⟩

01:27

If u is a unit vector,find 𝒖∙𝒗 and 𝒖∙𝒘.(Assume v and w are also unit vectors.)

01:27

Find 𝑎∙𝑏.|𝑎|=80, |𝑏|=70, the angle between a and b is 3𝜋/4.

01:27

Find 𝑎∙𝑏.|𝑎|=80, |𝑏|=50, the angle between a and b is 3𝜋/4.

01:27

Find 𝑎∙𝑏.|𝑎|=9, |𝑏|=4, the angle between a and b is 30^°.

01:27

Find 𝑎∙𝑏.|𝑎|=4, |𝑏|=8, the angle between a and b is 30^°.

00:58

Find 𝑎∙𝑏.𝑎=4𝑖+3𝑗−𝑘, 𝑏=−5𝑖+7𝑘

00:59

Find 𝑎∙𝑏.𝑎=4𝑖+5𝑗−𝑘, 𝑏=−5𝑖+7𝑘

00:59

Find 𝑎∙𝑏.𝑎=⟨5, 1, 1/5⟩, 𝑏=⟨9, −2, −10⟩

00:59

Find 𝑎∙𝑏.𝑎=3𝑖+𝑗, 𝑏=𝑖−6𝑗+𝑘

00:58

Find 𝑎∙𝑏.𝑎=3𝑖+𝑗, 𝑏=𝑖−9𝑗+𝑘

00:58

Find 𝑎∙𝑏.𝑎=⟨𝑝, −𝑝, 7𝑝⟩, 𝑏=⟨4𝑞, 𝑞, −𝑞⟩

00:59

Find 𝑎∙𝑏.𝑎=⟨𝑝, −𝑝, 9𝑝⟩, 𝑏=⟨4𝑞, 𝑞, −𝑞⟩

00:59

Find 𝑎∙𝑏.𝑎=⟨2, 1, 1/5⟩, 𝑏=⟨9, −3, −10⟩

00:59

Find 𝑎∙𝑏.𝑎=⟨5, −2⟩, 𝑏=⟨3, 6⟩

00:58

Find 𝑎∙𝑏.𝑎=⟨9, −4⟩, 𝑏=⟨5, 6⟩

03:26

Which of the following expression are meaningful? Which are meaningless? Explain.

01:54

Find v in component form.

04:56

Find the tension in each wire and the magnitude of each tension.

04:56

Find the tension in each wire and the magnitude of each tension.

04:57

Find the tension in each wire and the magnitude of each tension.

04:57

Find the tension in each wire and the magnitude of each tension.

02:27

Find the vector a with representation given by the directed line segment (𝐴𝐵) ⃗. A(-3, 5), B(6, 2)

02:00

If 𝑟=⟨𝑥, 𝑦, 𝑧⟩ and 𝑟0=⟨𝑥0, 𝑦0, 𝑧0 ⟩, describe the set of all points (x, y, z) such that |𝑟−𝑟0 |=9.

01:59

If 𝑟=⟨𝑥, 𝑦, 𝑧⟩ and 𝑟0=⟨𝑥0, 𝑦0, 𝑧0 ⟩, describe the set of all points (x, y, z) such that |𝑟−𝑟0 |=4.

01:59

If 𝑟=⟨𝑥, 𝑦, 𝑧⟩ and 𝑟0=⟨𝑥0, 𝑦0, 𝑧0 ⟩, describe the set of all points (x, y, z) such that |𝑟−𝑟0 |=6

01:28

Find a unit vector that is parallel to the line tangent to the parabola 𝑦=𝑥^2 at the point (4, 16).

01:29

Find a unit vector that is parallel to the line tangent to the parabola 𝑦=𝑥^2 at the point (2, 4).

03:56

Find the true course and the ground speed of the plane.

03:56

Find the true course and the ground speed of the plane.

03:55

Find the true course and the ground speed of the plane.

02:55

Find the magnitude of the resultant force and the angle it makes with the positive 𝑥−𝑎𝑥𝑖𝑠.

02:57

Find the magnitude of the resultant force and the angle it makes with the positive 𝑥−𝑎𝑥𝑖𝑠.

02:57

Find the magnitude of the resultant force and the angle it makes with the positive 𝑥−𝑎𝑥𝑖𝑠.

02:57

Find the magnitude of the resultant force and the angle it makes with the positive 𝑥−𝑎𝑥𝑖𝑠.

01:55

Find the horizontal and vertical components of the velocity vector.

02:01

Find the horizontal and vertical components of the velocity vector.

01:56

Find the horizontal and vertical components of the velocity vector.

02:26

Find the horizontal and vertical components of the force.

02:28

Find the horizontal and vertical components of the force.

02:28

Find the horizontal and vertical components of the force.

02:26

Find an equation of the set of all points equidistant from the points A(-2, 5, 2) and B(4, 3, -2)

00:57

Find v in component form.

00:58

Find v in component .

01:28

Find the vector a with representation given by the directed line segment (𝐴𝐵) ⃗. A(-5, 5), B(2, 4)

02:26

𝐹𝑖𝑛𝑑 𝑎+𝑏, 2𝑎+3𝑏, |𝑎|, 𝑎𝑛𝑑 |𝑎−𝑏|𝑎=𝑖+2𝑗−3𝑘, 𝑏=−2𝑖−𝑗+7𝑘

02:26

𝐹𝑖𝑛𝑑 𝑎+𝑏, 2𝑎+3𝑏, |𝑎|, 𝑎𝑛𝑑 |𝑎−𝑏|𝑎=𝑖+4𝑗−2𝑘, 𝑏=−5𝑖−𝑗+5𝑘

02:26

𝐹𝑖𝑛𝑑 𝑎+𝑏, 2𝑎+3𝑏, |𝑎|, 𝑎𝑛𝑑 |𝑎−𝑏|𝑎=𝑖+3𝑗−4𝑘, 𝑏=−3𝑖−𝑗+5𝑘

02:27

𝐹𝑖𝑛𝑑 𝑎+𝑏, 2𝑎+3𝑏, |𝑎|, 𝑎𝑛𝑑 |𝑎−𝑏|𝑎=2𝑖+𝑗, 𝑏=𝑖−2𝑗

01:27

What is the angle between the given vector and the positive direction of the 𝑥−𝑎𝑥𝑖𝑠?𝑖+√5𝑗

01:28

Find the vector that has the same direction as ⟨6, 2, −9⟩ but has length 5

01:27

Find a unit vector that has the same direction as the given vector.−9𝑖+2𝑗−𝑘