If p =2 i + k , q = i + j + k , r =4 i -3 j +7 k and a vector m is such that m q = r q , m p =0 , then m = .

Step-by-step solution

Given vectors are: p =2 i + k , q = i + j + k , r =4 i -3 j +7 k . From the condition m q = r q , we obtain ( m - r ) q = 0 . Since q 0 , it follows that m - r must be parallel to q , so m = r + q for some scalar . m = (4 i -3 j +7 k ) + ( i + j + k ) = (4+ ) i + (-3+ ) j + (7+ ) k Applying the condition m p = 0 yields: (4+ )(2) + (-3+ )(0) + (7+ )(1) = 0 8 + 2 + 7 + = 0 3 + 15 = 0 = -5 Substituting gives m = (-1) i + (-8) j + 2 k , which corresponds to option C. Final answer: C