Question

If \( \vec{a} = \hat{i} + 2\hat{j} + 2\hat{k} \), \( |\vec{b}| = 5 \) and the angle between \( \vec{a} \) and \( \vec{b} \) is \( \frac{\pi}{6} \), then the area of the triangle formed by these two vectors as two sides is:

• A. \( \frac{15}{4} \)
• B. \( \frac{15}{2} \)
• C. \( 15 \)
• D. \( \frac{15\sqrt{3}}{2} \)
• E. \( 15\sqrt{3} \)

Hint:

Remember that \( \frac{1}{2}|\vec{a} \times \vec{b}| \) is for a triangle, whereas \( |\vec{a} \times \vec{b}| \) gives the area of a parallelogram.

Answer 1

The Correct Option is A