Two vectors

→

x

and

→

y

are collinear if

→

x

= λ

→

y

, where λ is a constant
Now, the vectors 2

^

i

−3

^

j

+4

^

k

and a

^

i

+6

^

j

−8

^

k

are collinear
∴ 2

^

i

−3

^

j

+4

^

k

= λ . (a

^

i

+6

^

j

−8

^

k

) , where λ is a constant.
⇒ 2 = λ a , - 3 = 6 λ , 4 = - 8 λ
Now, - 3 = 6λ or 4 = - 8λ ⇒ λ = −

1

2

2 = λa
⇒ 2 = −

1

2

a
⇒ a = - 4