Question

If P(3,4,5), Q(4,6,3), R(-1,2,4), S(1,0,5), then the projection of RS on PQ is

• A. \(-2/3\)
• B. \(-4/3\)
• C. \(1/2\)
• D. 2

Hint:

Projection of \(\vec{a}\) on \(\vec{b}\) = \(\frac{\vec{a} \cdot \vec{b}}{|\vec{b}|}\).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Projection = \(\frac{\vec{RS} \cdot \vec{PQ}}{|\vec{PQ}|}\).
Step 2: Detailed Explanation:
\(\vec{PQ} = (1, 2, -2)\), \(|\vec{PQ}| = \sqrt{1 + 4 + 4} = 3\)
\(\vec{RS} = (2, -2, 1)\)
\(\vec{RS} \cdot \vec{PQ} = 2 - 4 - 2 = -4\)
Projection = \(-4/3\)
Step 3: Final Answer:
Projection = \(-4/3\).