Write the value of `p`for which ` vec a=3 hat i+2 hat j+9 hat k a n d vec b= hat i+p hat j+3 hat k`are parallel vectors.
Correct Answer – `p=2/3`
`vec(a) and vec(b) ” are parallel vectors ” hArr vec(a) xx vec(b) = vec(0).`
Correct Answer – `lambda=(2)/(3)`
Clearly ,`vec(a)||vec(b) hArr vec(a) xxvec(b)=vec(0)`.
`(vec(a)xxvec(b))=|(hat(i),hat(j),hat(k)),(1,lambda,3),(3,2,9)|=(9lambda-6)hat(i)-0hat(j)+(2-3lambda)hat(k)`
`:. (vec(a)xx vec(a)xxvec(b))=vec(0) hArr 9 lambda-6=0 and 2-3lambda=0 hArr lambda = (2)/(3)`.