If a-b-k-c-a-b- and the vectors -2-k-3-2-k-c- are coplanar- then -

The correct option is D 3 c⃗=λ (î 2ĵ+k̂)+μ (3î+2ĵ k̂) #160; (property of coplanar) c⃗=α (î+ĵ)+B(ĵ+k̂) 3μ +λ =α ———(1) λ μ =β #16 ...

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Condition for Coplanarity of Four Points

If a⃗=î+ĵ,b...

Question

If $\to a =^i +^j, \to b =^j +^k, \to c = α \to a + β \to b$ and the vectors $^i - 2^j +^k, 3^i + 2^j -^k, \to c$ are coplanar, then $\frac{α}{β} =$

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Solution

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\to a =^i +^j +^k, \to b =^i -^j + 2^k, \to c = x^i + (x - 2)^j -^k

x =

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\to b = 3^i + 2^j +^k

\to c =^i -^j - 4^k

\to d =^i + 2^j -^k

(\to a \times \to b) \times (\to c \times \to d) =

\to a = ˆ i + 2^j + 3^k, \to b = 2^i + 3^j +^k, \to c = 3^i +^j + 2^k

α \to a + β \to b + γ \to c = - 3 (^i -^k)

(α, β, γ)

\to a =^1 + 2^j + 3^k, \to b = 2^i + 3^j +^k, \to c = 3^i +^j + 2^k

α \to a + β \to b + γ \to c = - 3 (^i -^k) \cdot

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\to a =^i + 2^j +^k, \to b =^i -^j +^k, \to c =^i +^j -^k .

\to a

\to b

\to c

\frac{1}{\sqrt{3}}

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