BITSAT 2013 Paper

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