Determine whether u and v are orthogonal, parallel, or neither. $$\mathbf { u } = \langle 1,5 \rangle , \mathbf { v } = \langle - 25,2 \rangle$$
A) orthogonal
B) parallel
C) neither

Question

Quizplus · Accepted Answer

To determine if two vectors are orthogonal, we need to calculate their dot product. If the dot product is equal to 0, then the vectors are orthogonal. If the dot product is not 0, then the vectors are not orthogonal.

Let's calculate the dot product of u and v:

$\mathbf{u}\cdot\mathbf{v} = 1\cdot(-25) + 5\cdot2 = -23$

Since the dot product is not equal to 0, u and v are not orthogonal. To determine if they are parallel, we can check if one vector is a scalar multiple of the other.

Let's see if u is a scalar multiple of v:

$\dfrac{1}{-25} = \dfrac{5}{2}$

Since these two fractions are not equal, u is not a scalar multiple of v, and vice versa. Therefore, u and v are neither orthogonal nor parallel.

Determine Whether U and V Are Orthogonal, Parallel, or Neither u=⟨1,5⟩,v=⟨−25,2⟩\mathbf { u } = \langle 1,5 \rangle , \mathbf { v } = \langle - 25,2 \rangleu=⟨1,5⟩,v=⟨−25,2⟩

Determine Whether U and V Are Orthogonal, Parallel, or Neither $\mathbf { u } = \langle 1,5 \rangle , \mathbf { v } = \langle - 25,2 \rangle$