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The volume of parallelopiped whose edges are -12i+λk, 3i-k, 2i+j-15k respectively is 546, then λ=
- a)2
- b)1
- c)-3
- d)0
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The volume of parallelopiped whose edges are -12i+λk, 3i-k, 2i+...
Explanation:
The volume of a parallelepiped formed by three vectors a, b, and c is given by the scalar triple product of these vectors: V = |a ⨯ b ⋅ c|. Given the edges of the parallelepiped as -12i+λk, 3i-k, and 2i+j-15k, we can calculate the volume using the formula:
Calculation:
- Let a = -12i+λk, b = 3i-k, and c = 2i+j-15k
- Calculate the cross product of a and b: a ⨯ b = (|i j k|, -12 λ 0, 3 -1 0) = -12i - 12λj + 35k
- Calculate the dot product of a ⨯ b and c: (a ⨯ b) ⋅ c = (-12)(2) + (-12λ)(1) + (35)(-15) = -24 - 12λ - 525 = -12λ - 549
- Given that V = |(a ⨯ b) ⋅ c| = 546, we have |-12λ - 549| = 546
- Solve for λ: -12λ - 549 = ±546 => -12λ = 546 + 549 or -12λ = 549 - 546
- From the first equation, λ = 2.75, which does not satisfy the original equation, so we consider the second equation: λ = -3
Therefore, the correct value of λ is -3, making option C the correct answer.
The volume of a parallelepiped formed by three vectors a, b, and c is given by the scalar triple product of these vectors: V = |a ⨯ b ⋅ c|. Given the edges of the parallelepiped as -12i+λk, 3i-k, and 2i+j-15k, we can calculate the volume using the formula:
Calculation:
- Let a = -12i+λk, b = 3i-k, and c = 2i+j-15k
- Calculate the cross product of a and b: a ⨯ b = (|i j k|, -12 λ 0, 3 -1 0) = -12i - 12λj + 35k
- Calculate the dot product of a ⨯ b and c: (a ⨯ b) ⋅ c = (-12)(2) + (-12λ)(1) + (35)(-15) = -24 - 12λ - 525 = -12λ - 549
- Given that V = |(a ⨯ b) ⋅ c| = 546, we have |-12λ - 549| = 546
- Solve for λ: -12λ - 549 = ±546 => -12λ = 546 + 549 or -12λ = 549 - 546
- From the first equation, λ = 2.75, which does not satisfy the original equation, so we consider the second equation: λ = -3
Therefore, the correct value of λ is -3, making option C the correct answer.
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The volume of parallelopiped whose edges are -12i+λk, 3i-k, 2i+j-15k respectively is 546, then λ=a)2b)1c)-3d)0Correct answer is option 'C'. Can you explain this answer?
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The volume of parallelopiped whose edges are -12i+λk, 3i-k, 2i+j-15k respectively is 546, then λ=a)2b)1c)-3d)0Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The volume of parallelopiped whose edges are -12i+λk, 3i-k, 2i+j-15k respectively is 546, then λ=a)2b)1c)-3d)0Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The volume of parallelopiped whose edges are -12i+λk, 3i-k, 2i+j-15k respectively is 546, then λ=a)2b)1c)-3d)0Correct answer is option 'C'. Can you explain this answer?.
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