The magnitude of the projection of the vector on the vector perpendicular to the plane containing the vectors and is:
- A
- B
- C
- D
Solution & Step-by-step Explanation
1. Find the normal vector to the plane: $
\vec{a} = 2\hat{i} + 3\hat{j} + \hat{k} \vec{n} = \frac{|\vec{a} \cdot \vec{n}|}{|\vec{n}|}
$|\vec{a} \cdot \vec{n}| = |(2)(1) + (3)(-2) + (1)(1)| = |2 - 6 + 1| = |-3| = 3
.
\vec{a} = 2\hat{i} + 3\hat{j} + \hat{k} \vec{n} = \frac{|\vec{a} \cdot \vec{n}|}{|\vec{n}|}
$|\vec{a} \cdot \vec{n}| = |(2)(1) + (3)(-2) + (1)(1)| = |2 - 6 + 1| = |-3| = 3
.