Question

Find whether the vectors 2i+3j+4k and 4i+6j+8k are parallel or not?

Answer 1

Let a=2i+3j+4k
b=4i+6j+8k
b=2(2i+3j+4k)
b=2a
Therefore a & b are parallel

Answer 2

Two opposite vectors (in 3D space) will have a dab item equivalent to 0.

For the vectors 2i - 3j + 4k and ai + 6j - 8k, the dab item is: 2*a + (- 3)*6 + 4*(- 8) As they are opposite, which implies point between these two vectors is 90 degree.

In this way, their dab item is 0.

Hence, (2i-3j+4k).(ai+6j-8k)=0 Or, 2a-18– 32=0 Or, 2a=50 Or, a=25.