The sides of a parallelogram are represented by vectors p =5 i -4 j +3 k and q =3 i +2 j - k . Then, the area of the parallelogram is

Step-by-step solution

The area of a parallelogram with adjacent sides represented by vectors p and q is given by the magnitude of their cross product, | p q | . First, calculate the cross product p q : p q = vmatrix i & j & k 5 & -4 & 3 3 & 2 & -1 vmatrix Expanding the determinant: p q = i ((-4)(-1) - (3)(2)) - j ((5)(-1) - (3)(3)) + k ((5)(2) - (-4)(3)) p q = i (4 - 6) - j (-5 - 9) + k (10 + 12) p q = -2 i + 14 j + 22 k Now, calculate the magnitude of the resulting vector: | p q | = (-2)^2 + (14)^2 + (22)^2 | p q | = 4 + 196 + 484 | p