If `vec(a)=2hat(i)+2 hat(j)+3hat(k), vec(b)=-hat(i)+2hat(j)+hat(k) and vec(c)=3hat(i)+hat(j)` are three vectors such that `vec(a)+t vec(b)` is perpendicular to `vec(c)`, then what is t equal to ?

Options

A. 8
B. 6
C. 4
D. 2

Answer

A

Explanation

`vec(a)+t vec(b)=(2-t)hat(i)+(2+2t)hat(j)+(3+t)hat(k)`
`(vec(a)+t vec(b)) and vec(c)` is perpendicular. Therefore,
`(vec(a)+t vec(b)).vec(c)=0`
`3(2-t)+2+2t=0`
`6-3t+2t+2=0`
`t=8`