Question

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

Answer 1

Answer:

For a = -4 the two given vectors are collinear.

Step-by-step explanation:

Given: Vectors  $2\hat{i}-3\hat{j}+4\hat{k}$ and $a\hat{i}+6\hat{j}-8\hat{k}$

We have to find the value of a for which two given vectors are collinear.

Two vectors are said to be collinear if one vector can be expressed as a constant multiple of other vector.

Consider the given vectors

 $2\hat{i}-3\hat{j}+4\hat{k}$ and $a\hat{i}+6\hat{j}-8\hat{k}$

Clearly,   $a\hat{i}+6\hat{j}-8\hat{k}=n(2\hat{i}-3\hat{j}+4\hat{k})$

Comparing, we get,

a = 2n

6 = -3n

-8 = 4n

Thus, n = -2

Thus, a = -4

Thus, for a = -4 the two given vectors are collinear.