Question:
The projection of the vector \( \mathbf{i} - 2\mathbf{j} + \mathbf{k} \) on the vector \( 4\mathbf{i} - 4\mathbf{j} + 7\mathbf{k} \) is:
The projection of the vector \( \mathbf{i} - 2\mathbf{j} + \mathbf{k} \) on the vector \( 4\mathbf{i} - 4\mathbf{j} + 7\mathbf{k} \) is:
Show Hint
Use the projection formula to find the component of one vector along another.
Updated On: Jan 6, 2026
- \( \frac{5\sqrt{6}}{10} \)
- \( \frac{19}{9} \)
- \( \frac{9}{19} \)
- \( \frac{\sqrt{6}}{19} \)
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The Correct Option is B
Solution and Explanation
Step 1: Use the formula for the projection.
The formula for the projection of a vector on another is: \[ \text{proj}_v(u) = \frac{u \cdot v}{|v|^2} v \]
Step 2: Conclusion.
After performing the calculation, we find the projection is \( \frac{19}{9} \).
Final Answer: \[ \boxed{\frac{19}{9}} \]
The formula for the projection of a vector on another is: \[ \text{proj}_v(u) = \frac{u \cdot v}{|v|^2} v \]
Step 2: Conclusion.
After performing the calculation, we find the projection is \( \frac{19}{9} \).
Final Answer: \[ \boxed{\frac{19}{9}} \]
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