Determine whether the vectors a and b are​ parallel, orthogonal, or neither:

Question

Determine whether the vectors a and b are parallel, orthogonal, or neither:

a=⟨3,5⟩ and b=⟨-10,-6⟩

Answer 1

If orthogonal, their dot product is zero.

 

If parallel, their dot product is the product of their magnitudes.

 

In anti-parallel, their dot product is the negative of the product of their magnitudes.

 

Test them.

 

|a| = √(3² + 5²) = √34

|b| = √[(-10)² + (-6)²] = √136 = 2√34

|a| |b| = (√34)(2√34) = 68

a·b = (3)(-10) + (5)(-6) = -30 - 30 = -60

 

It looks like neither.