Write the value of `p`for which ` vec a=3 hat i+2 hat j+9 hat k a n d – InterviewSolution

InterviewSolution

1.	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.
Answer» 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)`.

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