Two vectors lie with their tails at the same point.When the angle between them is increased by 20° the magnitude of their vector product doubles.The original angle between them was about:
A)0°
B)18°
C)25°
D)45°
E)90°

Question

Quizplus · Accepted Answer

The magnitude of the vector product (or cross product) of two vectors is given by |A×B| = |A||B|sin(θ), where |A| and |B| are the magnitudes of the vectors and θ is the angle between them. If doubling the magnitude of their vector product requires increasing the angle by 20°, we can set up the equation |A||B|sin(θ + 20°) = 2|A||B|sin(θ). Simplifying, we get sin(θ + 20°) = 2sin(θ). Without solving this equation explicitly, we know that the solution must be a relatively small angle because the sine function increases as the angle increases from 0° to 90°, and doubling the sine of an angle by only increasing the angle by 20° suggests the original angle is not too large. Among the given options, 18° is the one that fits this description and is a plausible solution to the equation under these conditions.

Two Vectors Lie with Their Tails at the Same Point