Question:
If vectors \( 2i + j + k \), \( 2j - 3k \), and \( 3i + j + 5k \) are coplanar, then the value of \( a \) is
If vectors \( 2i + j + k \), \( 2j - 3k \), and \( 3i + j + 5k \) are coplanar, then the value of \( a \) is
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For three vectors to be coplanar, their scalar triple product must be zero.
Updated On: Mar 25, 2026
- 2
- -2
- 4
- -4
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The Correct Option is D
Solution and Explanation
Step 1: Use the condition for coplanarity.
Three vectors are coplanar if their scalar triple product is zero. Calculate the scalar triple product and set it equal to zero to solve for \( a \).
Step 2: Conclusion.
After performing the calculation, we find that \( a = -4 \). Final Answer: \[ \boxed{-4} \]
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