If vectors 2î − ĵ + k̂, î + 2ĵ − 3k̂ and 3î + λĵ + 5k̂ are coplanar, then the value of λ is: A. 4 B. −4 C. 2 D. −2 Answer: B) −4 Explanation: For coplanar vectors, their scalar triple product is zero. Det: 2(10 + 3λ) − (−1)(5 + 9) + 1(λ − 6) = 0. 20 + 6λ + 14 + λ − 6 = 0. 7λ + 28 = 0. λ = −4.

imo class 12 vector algebra

If vectors 2î − ĵ + k̂, î + 2ĵ − 3k̂ and 3î + λĵ + 5k̂ are coplanar, then the value of λ is:

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If vectors 2î − ĵ + k̂, î + 2ĵ − 3k̂ and 3î + λĵ + 5k̂ are coplanar, then the value of λ is:

A. 4
B. −4
C. 2
D. −2

Answer: B) −4

Explanation: For coplanar vectors, their scalar triple product is zero. Det: 2(10 + 3λ) − (−1)(5 + 9) + 1(λ − 6) = 0. 20 + 6λ + 14 + λ − 6 = 0. 7λ + 28 = 0. λ = −4.

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