Question

If vectors 5i + 7j - 3k and 2i -bj + ck are parallel then what is the value of b and c?

Answer 1

hey mate
here's the solution

Answer 2

We  know  that, if  two vectors (A and B) are  parallel to each other than,

A = K(B)

Let,

$A=5i+7j-3k\\\;\\B=2i-bj+ck$

If  A  and  B are  parallel,

$A=K(B)\\\;\\5i+7j-3k=K(2i-bj+ck)\\\;\\5i+7j-3k=2Ki-bKj+cKk\\\;\\\text{On Camparing coefficients of unit vectors i, j and k}\\\;\\5=2k\implies k=\frac{5}{2}\\\;\\7=-bk\implies 7=-\frac{5}{2}\times b\implies b=\frac{-14}{5}\\\;\\-3=ck\implies-3=c\times\frac{5}{2}\implies c=\frac{-6}{5}$

Hence,

$b=\frac{-14}{5}\\\;\\c=\frac{-6}{5}$