What is the area of the parallelogram whose sides are represented by the vectors i + 2 j + 3 k and 2 i + j + 2 k ?

Step-by-step solution

Let a = i + 2 j + 3 k and b = 2 i + j + 2 k . The area of the parallelogram with adjacent sides a and b is given by | a b | . a b = vmatrix i & j & k 1 & 2 & 3 2 & 1 & 2 vmatrix = i (4 - 3) - j (2 - 6) + k (1 - 4) = i + 4 j - 3 k The magnitude of the cross product is: | a b | = 1^2 + 4^2 + (-3)^2 = 1 + 16 + 9 = 26 The area of the parallelogram is 26 square units. Answer: 26 square units