Question

Vector \(\vec{A}\) of magnitude \(5 \sqrt{3}\) units, another vector \(\vec{B}\) of magnitude of 10 units are inclined to each other at an angle of \(30^{\circ}\). The magnitude of vector product of the two vectors is \(\left[\sin 30^{\circ}=\frac{1}{2}\right]\)

• A. \(5\sqrt{3}\) units
• B. 10 units
• C. \(25\sqrt{3}\) units
• D. 75 units

Hint:

Use the magnitude of the cross product, AB sin of the angle between them.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
\(|\vec A\times\vec B|=AB\sin\theta\).

Step 2: Substitute
\(A=5\sqrt3,\ B=10,\ \theta=30^{\circ}\) with \(\sin30^{\circ}=\dfrac12\).

Step 3: Calculation
\(|\vec A\times\vec B|=5\sqrt3\times10\times\dfrac12=25\sqrt3\) units.

Step 4: Compare the options
This is option (C).

Final Answer:
The magnitude of the vector product is \(25\sqrt3\) units. \[ \boxed{\text{(C) }25\sqrt{3}\ \text{units}} \]