Determine whether u and v are orthogonal, parallel or neither. $$\mathbf { u } = 18 \mathbf { i } + 6 \mathbf { j } , \mathbf { v } = 5 \mathbf { i } - 15 \mathbf { j }$$
A) Parallel, same direction
B) Orthogonal
C) Neither parallel nor orthogonal
D) Parallel, opposite direction

Question

Quizplus · Accepted Answer

To check whether two vectors are orthogonal, we need to calculate their dot product. If the dot product is zero, then the vectors are orthogonal. If the dot product is non-zero, then the vectors are not orthogonal. 
The dot product of u and v is: 
u . v = (18)(5) + (6)(-15) = 90 - 90 = 0  
Since the dot product is zero, u and v are orthogonal.

Determine Whether U and V Are Orthogonal, Parallel or Neither u=18i+6j,v=5i−15j\mathbf { u } = 18 \mathbf { i } + 6 \mathbf { j } , \mathbf { v } = 5 \mathbf { i } - 15 \mathbf { j }u=18i+6j,v=5i−15j

Determine Whether U and V Are Orthogonal, Parallel or Neither $\mathbf { u } = 18 \mathbf { i } + 6 \mathbf { j } , \mathbf { v } = 5 \mathbf { i } - 15 \mathbf { j }$