Question

Prove that if the vector A and B are parallel to each other than A.B=AB

Answer 1

Answer:

A.B is the dot product of A&B,

important thing to note is that dot product is the projection of

vector A on B or vice versa.

Also the formula of dot product is,

|A.B| = |A| |B| cos(theta),

where theta is the angle between vectors A & B.

Using the formula,

A.B = AB,

for theta = 0 degrees.

Explanation:

Answer 2

Answer:

The two vectors should be scalar multiples of each other. For example consider the vectors: v1=(1,2,3)v1=(1,2,3) and v2=(2,4,6)v2=(2,4,6) . These vectors are parallel to each other and we can easily show that v2=2⋅v1.v2=2⋅v1. This means that v1v1 and v2v2 have the same direction (hence parallel), but only differ in magnitude. Showing this will suffice.