If the vectors `2hat(i)-qhat(j)+3hat(k)and4hat(i)-5hat(j)+6hat(k)` are collinear, then of q is

Options

A. 5
B. 10
C. `5/2`
D. `5/4`

Answer

C

Explanation

Let `a=2hat(i)-qhat(j)+3hat(k)` and `b=4hat(i)-5hat(j)+6hat(k)`.
Since vectors are collinear so they will be scalar multiple of each other .
`vec(a)=R vec(b)`
`2hat(i)-qhat(j)+3hat(k)=R(4hat(i)-5hat(j)+6hat(k))`
`2hat(i)-1hat(j)+3hat(k)=4Rhat(i)-5Rhat(j)+6R hat(k)`
On comparing, we get
`4R=2`
`rArr R=1/2`
`-5R=-q`
`rArr 5xx(1)/(2)=q`
`rArr q=(5)/(2)`
Hence, correct answer from the given alternatives is (c).