Three point A, B and C with position vectors `a_(1)=3hati-2hatj-hatk, a_(2)=hati+3hatj+4hatk and a_(3)=2hati+hatj-2hatk` relative to an origin O. The distance of A from the plane OBC is (magnitude)

Options

A. 5
B. `sqrt3`
C. 3
D. `2sqrt3`

Answer

C

Explanation

Equation of plane `OBC= a_(1) = alpha a_(2) +beta a_(3)`,
i.e., `a_(1)*(a_(2)xxa_(3))=0`
The distance of A from the plane `OBC = |(a_(1)*(a_(2)xxa_(3)))/(|a_(2)xxa_(3)|)|`
`a_(2)xxa_(3) = -10hati + 10 hatj - 5hatk`
`rArr | a_(2) xx a_(3)|=15`
`therefore ` Distance ` = (1)/(15) ||(3,-2,-1),(1,3,4),(2,1,-2)||=3`