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Question

If a=^i+2^j+4^k, b=^i+λ^j+4^k, c=2^i+4^j+(λ21)^k, are coplanar vectors and a,c are not parallel, then |a×c| is equal to

A
35
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B
25
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C
25
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D
55
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Solution

The correct option is D 55
Given: a,b,c are coplanar.
∣ ∣1241λ424λ21∣ ∣=0
1(λ(λ21)16)2(λ218)+4(42λ)=0
λ32λ29λ+18=0
(λ2)(λ29)=0
λ=2 or λ=±3
But for λ=±3, a is parallel to c.
So, λ=2
a×c=∣ ∣ ∣^i^j^k124243∣ ∣ ∣
a×c=^i(616)^j(38)+^k(44)
a×c=10^i+5^j
Now, |a×c|=100+25=55

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