If the points with position vectors `10 hat i+3 hat j ,12 hat i-5 hat j` and `a hat i+11 hat j` are collinear, find the value of `adot`

Options

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

Answer

C

Explanation

Since, the points with position vectors `10hat(i)+3hat(j), 12hat(i)-5hat(j), ahat(i)+11hat(j)` are collinear.
` :. |(10,3,1),(12,-5,1),(a, 11,1)|=0`
`rArr 10(-5-11)-3(12-a)+1(132+5a)=0`
`rArr -160-36+3a+132+5a=0`
`rArr -196+132+8a=0`
`rArr 8a=64`
`rArr a=8`