For what value of ‘a’ the vectors 2i - 3j + 4k and ai + 6j - 8k are collinear ?

Question

For what value of  ‘a’  the vectors  \(2\hat i-3\hat j+4\hat k\)  and  \(a\hat i+6\hat j-8\hat k\)  are collinear ?

Answer 1

Two vectors  \(\vec a=a_1\hat i+a_2\hat j+a_3\hat k\)  and  \(\vec b=b_1\hat i+b_2\hat j+b_3\hat k\) are collinear, if and only if 

Here \(\vec a=2\hat i-3\hat j+4\hat k\)  and \(\vec b=a\hat i+6\hat j-8\hat k\)

Hence, 

Solving this equality, we get

a = -4