Question

Find the value of a for which the vectors 3i+3j+9k and i+aj+3k are parallel

Answer 1

Two vectors are parallel, if one vector is scalar multiple of other. Thus,
$\frac{3}{1} = \frac{3}{a} = \frac{9}{3} \\ \frac{3}{a} = 3 \\ a = 1$

Answer 2

Thus For two vectors to be parallel, the components of the vector should be known as each other.

If vectors A=2i+2j+3k and B=3i+6k+nk are perpendicular to each other the value can determined.

Yes these are parallel vectors because if we multiple in second with 3,

we get b= 3i+6j+9k which is Vector a=2i+3j+4k, and vector b=3i+4j+5k.