For vectors a and b, given that $| \mathbf { a } \times \mathbf { b } | = | \mathbf { a } | | \mathbf { b } |$ , which of the following statements is true?
A)a and b are parallel
B)a and b are not parallel
C)a = b

D)a and b are perpendicular
E)a and b are not perpendicular

Question

For vectors a and b, given that $| \mathbf { a } \times \mathbf { b } | = | \mathbf { a } | | \mathbf { b } |$ , which of the following statements is true?
A)a and b are parallel
B)a and b are not parallel
C)a = b

D)a and b are perpendicular
E)a and b are not perpendicular

Quizplus · Accepted Answer

The magnitude of the cross product $| \mathbf { a } \times \mathbf { b } |$ equals the product of the magnitudes of the vectors $| \mathbf { a } | | \mathbf { b } |$, and the sine of the angle between them. This equation holds true when the sine of the angle is 1, which happens when the vectors are perpendicular (90 degrees apart).

For Vectors a and B, Given That ∣a×b∣=∣a∣∣b∣| \mathbf { a } \times \mathbf { b } | = | \mathbf { a } | | \mathbf { b } |∣a×b∣=∣a∣∣b∣

For Vectors a and B, Given That $| \mathbf { a } \times \mathbf { b } | = | \mathbf { a } | | \mathbf { b } |$