State if the vectors a and b are perpendicular, parallel, or neither. If a and b are parallel, state whether they point in the
same direction or in opposite directions.
-a = 7, 4 , b = 5, 1
A) Perpendicular
B) Parallel, same direction
C) Parallel, opposite directions
D) Neither

Question

Quizplus · Accepted Answer

Two vectors are perpendicular if their dot product is zero. They are parallel if one is a scalar multiple of the other. The dot product of vectors a and b is $7*5 + 4*1 = 35 + 4 = 39$, which is not zero, so they are not perpendicular. Vector b is not a scalar multiple of vector a (since $7/5 \neq 4/1$), so they are not parallel. Therefore, the vectors are neither perpendicular nor parallel.

State If the Vectors a and B Are Perpendicular, Parallel