Practice: Dot Product

10 multiple choice · 4 free response · 1 walkthroughs

Q1.

basic

Find

⟨ 2, 3, - 1 ⟩ \cdot ⟨ 4, - 2, 5 ⟩

Q2.

basicExam 1 Review #3

Are

u = ⟨ 3, 1, - 1 ⟩

and

v = ⟨ 2, 4, 10 ⟩

orthogonal?

Q3.

basic

∣ u ∣ = 3, ∣ v ∣ = 4

, and the angle between them is

60°

, then

u \cdot v =

Q4.

intermediate

The scalar projection of

u

onto

v

(the signed length) equals

Q5.

basic

u \cdot v < 0

, the angle between them is

Q6.

basic

Compute

v \cdot v

v = ⟨ 1, - 2, 2 ⟩

Q7.

basic

Find work done by

F = ⟨ 3, - 2, 1 ⟩

moving an object from

(0, 0, 0)

(2, 4, - 1)

Q8.

intermediate

Find a unit vector orthogonal to both

u = ⟨ 1, 0, 0 ⟩

and

v = ⟨ 0, 1, 0 ⟩

Q9.

basic

Determine the value of

c

that makes

⟨ 2, c, - 1 ⟩

orthogonal to

⟨ 3, 4, 1 ⟩

Q10.

basic

True/False:

(u + v) \cdot w = u \cdot w + v \cdot w