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
- \( \frac{5\sqrt{6}}{10} \)
- \( \frac{19}{9} \)
- \( \frac{9}{19} \)
- \( \frac{\sqrt{6}}{19} \)
Hide Solution
Verified By Collegedunia
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: \[ \boxed{\frac{19}{9}} \]
Was this answer helpful?
0
0
Top Questions on Vectors
- For three non–coplanar vectors \(\vec a,\vec b,\vec c\), if \[ (\vec b+\vec c)\cdot\big((\vec c+\vec a)\times(\vec a+\vec b)\big) = \alpha \,[\vec a\,\vec b\,\vec c] \] and \[ (\vec a+\vec b)\cdot\big((\vec b+\vec c)\times(\vec a+\vec b+\vec c)\big) = \beta \,[\vec a\,\vec b\,\vec c], \] then \(\alpha+\beta\) is equal to:
- Let \(\alpha,\beta,\gamma\ (0<\alpha,\beta,\gamma<\tfrac{\pi}{2})\) be the angles between non–zero vectors \(\vec a\) and \(\vec b\), \(\vec b\) and \(\vec c\), \(\vec c\) and \(\vec a\) respectively. If \(\theta\) is the angle that the vector \(\vec a\) makes with the plane containing \(\vec b\) and \(\vec c\), then:
- If position vector is given as \(\vec{r} = x\hat{i} + y\hat{j} + z\hat{k}\) and if its signs are reversed, then which of the following physical quantity remains unaffected?
- A vector \( \mathbf{a} \) makes equal angles with all the three axes. If the magnitude of the vector is \( 5\sqrt{3} \) units, then find \( \mathbf{a} \).
- If \( \overrightarrow{a} + \overrightarrow{b} + \overrightarrow{c} = 0 \), \( |\overrightarrow{a}| = \sqrt{37} \), \( |\overrightarrow{b}| = 3 \), and \( |\overrightarrow{c}| = 4 \), then the angle between \( \overrightarrow{b} \) and \( \overrightarrow{c} \) is:
View More Questions
Questions Asked in VITEEE exam
- Find the value of \( x \) in the following equation: \[ \frac{2}{x} + \frac{3}{x + 1} = 1 \]
- VITEEE - 2025
- Algebra
- In a code language, 'TIGER' is written as 'JUISF'. How will 'EQUAL' be written in that language?
- VITEEE - 2025
- Data Interpretation
- TUV : VYB :: PRA : ?
- VITEEE - 2025
- Odd one Out
- What is the pH of a solution with a \( \text{H}^+ \) concentration of \( 1 \times 10^{-3} \) mol/L?
- VITEEE - 2025
- Solubility Equilibria Of Sparingly Soluble Salts
- In a code language, 'TIGER' is written as 'JUISF'. How will 'EQUAL' be written in that language?
- VITEEE - 2025
- Odd one Out
View More Questions