Mathematics - Vector Question with Solution | TestHub

If given vectors are coplanar, then there exists two scalar quantities $\mathrm{x}$ and $\mathrm{y}$ such that $2\hat{i}-\hat{j}+\hat{k}=x(\hat{i}+2\hat{j}-3\hat{k})+y(3\hat{i}+a\hat{j}+5\hat{k})$ Comparing coefficient of $\hat{i},\hat{j}$ and $\hat{k}$ on both sides of (1) we get $x+3y=2,2x+ay=-1,-3x+5y=1\dots (2)$ Solving first and third equations, we get $\mathrm{x}=1/2,\mathrm{y}=1/2$ Since the vectors are coplanar, therefore these values of $x$ and $y$ will satisfy the equation $2x+ay=-1$ $\therefore 2(1/2)+a(1/2)=-1\Rightarrow a=-4$