The area of a triangle formed by vectors P = (3 i - 4 j + 2 k ) m and Q = ( i + j - 2 k ) m as adjacent sides is approximately

Step-by-step solution

The area of a triangle with adjacent sides P and Q is given by 1 2 | P Q | . Calculating the cross product of the given vectors: P Q = vmatrix i & j & k 3 & -4 & 2 1 & 1 & -2 vmatrix P Q = i (8 - 2) - j (-6 - 2) + k (3 + 4) = 6 i + 8 j + 7 k Finding the magnitude of the cross product: | P Q | = 6^2 + 8^2 + 7^2 = 36 + 64 + 49 = 149 The area of the triangle is: Area = 1 2 149 12.2 2 = 6.1 Approximating to the nearest integer, the numerical value of the area is 6 . Answer: 6 m ^2