If the volume of a parallelepiped whose adjacent edges are \( a\) = 2î + 3ĵ + 4k̂ \( b\) = î + αĵ + 2k̂ \( c\) = î + 2ĵ + αk̂ is 15 then α = ?

Volume: \[ | ccc 2 & 3 & 4 \\ 1 & α & 2 \\ 1 & 2 & α | = 15 \] \[ 2(α 2 - 4) - 3(α - 2) + 4(2 - α) = 15 \] \[ 2α 2 - 7α - 9 = 0 \] \[ (α + 1)(2α - 9) = 0 \] Hence: \[ α = -1, 9/2 \]

If the volume of a parallelepiped... - Solved

Question 37

Mathematics Scalar and Vector Products Hard

If the volume of a parallelepiped whose adjacent edges are \(\rm \vec a\) = 2î + 3ĵ + 4k̂ \(\rm \vec b\) = î + αĵ + 2k̂ \(\rm \vec c\) = î + 2ĵ + αk̂ is 15 then α = ?

(A) 1

(B) \(\dfrac52\)

(C) \(\dfrac92\)

(D) 0

✓ Correct Answer: Option C Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

Volume: \[ \left| \begin{array}{ccc} 2 & 3 & 4 \\ 1 & \alpha & 2 \\ 1 & 2 & \alpha \end{array} \right| = 15 \] \[ \Rightarrow 2(\alpha^2 - 4) - 3(\alpha - 2) + 4(2 - \alpha) = 15 \] \[ \Rightarrow 2\alpha^2 - 7\alpha - 9 = 0 \] \[ \Rightarrow (\alpha + 1)(2\alpha - 9) = 0 \] Hence: \[ \alpha = -1, \quad \frac{9}{2} \]

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Question 37

📘 Step-by-Step Solution & Detailed Explanation:

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