Question:
If the scalar product of two vectors $x\hat{i} + 3\hat{j} + 2\hat{k}$ and $2\hat{i} - 3\hat{j} + 4\hat{k}$ is 9, then the value of $x$ is:
If the scalar product of two vectors $x\hat{i} + 3\hat{j} + 2\hat{k}$ and $2\hat{i} - 3\hat{j} + 4\hat{k}$ is 9, then the value of $x$ is:
Show Hint
Dot product equals sum of products of corresponding components.
Updated On: Apr 24, 2026
- $9$
- $5$
- $6$
- $1$
- $2$
Show Solution
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The Correct Option is B
Solution and Explanation
Concept:
• Dot product: \[ \vec{a}\cdot\vec{b} = x_1x_2 + y_1y_2 + z_1z_2 \]
Step 1: Compute dot product
\[ = x(2) + 3(-3) + 2(4) \] \[ = 2x - 9 + 8 = 2x - 1 \]
Step 2: Equate
\[ 2x - 1 = 9 \] \[ 2x = 10 \Rightarrow x = 5 \] Final Conclusion:
\[ x = 5 \]
• Dot product: \[ \vec{a}\cdot\vec{b} = x_1x_2 + y_1y_2 + z_1z_2 \]
Step 1: Compute dot product
\[ = x(2) + 3(-3) + 2(4) \] \[ = 2x - 9 + 8 = 2x - 1 \]
Step 2: Equate
\[ 2x - 1 = 9 \] \[ 2x = 10 \Rightarrow x = 5 \] Final Conclusion:
\[ x = 5 \]
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