Suppose U = <2,3,4> Then:

Question

<4,5,3> makes a (right, obtuse, or acute) with u.

<5,-1,2> makes a (right, obtuse, or acute) with u.

<-8,0,4> makes a (right, obtuse, or acute) with u.

<3,2,-3> makes a (right, obtuse or acute) with u.

 

I would like to know how to solve these, but I have no clue on how to do that. Thank you to any help!

Answer 1

You have some vectors in the form

 

A = <A_x, A_y, A_z>

 

Evaluate the "dot" product of each vector A with U.

 

A·U = A_xU_x + A_yU_y + A_zU_z

 

Plug in the numbers, set equal to another form of the dot product:

 

A·U = |A| |U| cosθ,

 

where θ is the angle between the vectors, and

 

|A| = √(A_x² + A_y² + A_z²)

 

You now have enough information to find cosθ.  The conditions you want to look at are:

 

cosθ = 0 ⇒ right angle 

cosθ > 0 ⇒ accute

cosθ < 0 ⇒ obtuse