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a→ and c→ are unit vector and |b→|=4 .the angle between a→ and c→ is cos−1⁡(1/4) and b→−2c→=λa→ the value of λ is

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a

3,- 4

b

14,34

c

-3, 4

d

-14,34

answer is A.

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Detailed Solution

b→−2c→=λa→ or b→=2c→+λa→ or |b→|2=|2c→+λa→|2⇒ 16=4|c→|2+λ2|a→|2+4λa→⋅c→ =4+λ2+4λ14 or λ2+λ−12=0 or λ=3,−4

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