Vector Algebra · Question 6

Let OP= -1 i+ j+ k, OQ= i+ -1 j+ k and OR= i+ j+ 12 k be three vectors, where , R-\0\ and O denotes the origin. If ( OP OQ ) OR=0 and the point ( , ,2) lies on the plane 3x+3y-z+l=0, then the value of l is .

Answer

5

Solution

Let p= -1 , q= -1 .

vmatrix p & 1 & 1 \ 1 & q & 1 \ 1 & 1 & 12 vmatrix= pq2-p-q+ 32=0 (p-2)(q-2)=1

p-2=- 1+ , q-2=- 1+ (1+ )(1+ )= + =-1

3 +3 -2+l=0 -3-2+l=0 l=5

Answer: 5