For what value of m are the points with position vectors `10hat(i)+3hat(j), 12hat(i)-5hat(j) and m hat(i)+11 hat(j)` collinear ?

Options

A. -8
B. 4
C. 8
D. 12

Answer

C

Explanation

Let `vec(A) = 10hat(i)+3hat(j), vec(B)=12hat(i)-5hat(j)`
and `vec(C)=mhat(i)+11hat(j)`
Now, `vec(A)B=2hat(i)-8hat(j) and vec(B)C=(m-12)hat(i)+16hat(j)`
`vec(A)Bxxvec(B)C=|(hat(i), hat(j), hat(k)), (2,-8,0),(m-12, 16, 0)|=0`
`=hat(i)(0)-hat(j)(0)+hat(k)(32+8m-96)`
`=k(-64+8m)=0rArr8m=64`
`rArr m=8`