The lengths of two vectors a and b, and the angle $\theta$ between them, are given. Find the length of their cross product, $| \mathbf { a } \times \mathbf { b } |$ . $| \mathbf { a } | = 4 , \mathbf { b } \mid = 5 , \theta = 60 ^ { \circ }$
A) $20 \sqrt { 3 }$
B) $10 \sqrt { 2 }$
C) $10 \sqrt { 3 }$
D) $10$
E) none of these

Question

Quizplus · Accepted Answer

The length of the cross product of two vectors is given by $| \mathbf { a } \times \mathbf { b } | = | \mathbf { a } | | \mathbf { b } | \sin \theta$. Substituting the given values: $4 \times 5 \times \sin 60^\circ = 20 \times \frac{\sqrt{3}}{2} = 10 \sqrt{3}$.

The Lengths of Two Vectors a and B, and the Angle