Question:
The length of a vector $(3\hat{i} + \hat{j} + 2\hat{k})$ in XY plane is
The length of a vector $(3\hat{i} + \hat{j} + 2\hat{k})$ in XY plane is
Show Hint
To find the length in any specific plane (XY, YZ, or ZX), simply zero out the component not mentioned and calculate the magnitude.
Updated On: Jul 4, 2026
- $\sqrt{14}$
- 2
- $\sqrt{10}$
- $\sqrt{5}$
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The Correct Option is C
Solution and Explanation
Step 1: Concept
The projection of a vector $\vec{A} = x\hat{i} + y\hat{j} + z\hat{k}$ in the XY plane is $x\hat{i} + y\hat{j}$.
Step 2: Meaning
The "length in the XY plane" refers to the magnitude of this projection, ignoring the $z$ component.
Step 3: Analysis
For the vector $(3\hat{i} + \hat{j} + 2\hat{k})$, the components in the XY plane are $x=3$ and $y=1$. Magnitude = $\sqrt{x^{2} + y^{2}}$.
Step 4: Conclusion
Magnitude = $\sqrt{3^{2} + 1^{2}} = \sqrt{9 + 1} = \sqrt{10}$. Final Answer: (C)
The projection of a vector $\vec{A} = x\hat{i} + y\hat{j} + z\hat{k}$ in the XY plane is $x\hat{i} + y\hat{j}$.
Step 2: Meaning
The "length in the XY plane" refers to the magnitude of this projection, ignoring the $z$ component.
Step 3: Analysis
For the vector $(3\hat{i} + \hat{j} + 2\hat{k})$, the components in the XY plane are $x=3$ and $y=1$. Magnitude = $\sqrt{x^{2} + y^{2}}$.
Step 4: Conclusion
Magnitude = $\sqrt{3^{2} + 1^{2}} = \sqrt{9 + 1} = \sqrt{10}$. Final Answer: (C)
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