Question

If vector p=xi+3j+2k is coplanar with vectors a=2i=2j+3k & b=2i+3j+4k,
then find the value of x.

Answer 1

\[\hat{p}=x\hat{i}+3\hat{j}+2\hat{k}\]\[\hat{a}=2\hat{i}+2\hat{j}+3\hat{k}\]\[\hat{b}=2\hat{i}+3\hat{j}+4\hat{k}\]\[\hat{a}\times\hat{b}=\left(\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\2&2&3\\2&3&4\end{array}\right)=-\hat{i}-2\hat{j}+2\hat{k}\]\[(\hat{a}\times\hat{b})\cdot\hat{p}=-x-6+4=-x-2=0\quad\Rightarrow\quad x=-2\]

Answer 2

is your vector a = 2i + 2j... or 2i - 2j...

Answer 3

nevermind...