Question

Given 2 vectors a and b, which of the following statement(s) is/are correct?

A) The dot product of vectors a and b is zero.
B) The cross product of vectors a and b is a scalar.
C) Vectors a and b are orthogonal.
D) The magnitude of vector a is equal to the magnitude of vector b.

Answer 1

The dot product of vectors a and b determines if they are orthogonal. The cross product of vectors a and b is a vector, not a scalar.

Step-by-step explanation:

The dot product of vectors a and b is given by the equation:

a · b = |a| · |b| · cos(θ)

If the dot product of vectors a and b is zero (a · b = 0), then the vectors are orthogonal, which means they are perpendicular to each other. So, statement C is correct. However, this does not imply that the magnitude of vector a is equal to the magnitude of vector b (statement D).

The cross product of vectors a and b is a vector, not a scalar. The direction of the cross product is perpendicular to both vectors. So, statement B is incorrect.