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Question

If the four points with position vectors 2^i+^j+^k, ^i+^j+^k, ^j^k and λ^j+^k are coplanar, then λ=

A
1
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B
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C
1
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D
0
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Solution

The correct option is A 1
Let the four given points be
a=2^i+^j+^k,b=^i+^j+^k,c=^j^k,d=λ^j+^k

From the given points, we can conclude
ba=3^icb=^i2^kdc=(λ1)^j+2^k

Since, the given points are co-planar
∣ ∣3001020λ12∣ ∣=0

6(1λ)=0λ=1

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