Let a - c be unit vectors and - b -4- The angle between a and c is cos -11-4- Then the positive integral value of - Such that b-2 c - a is

(b̅)^2=(2 c̅ + λa̅)^2 ⇒ |b̅|^2 = 4 |c̅|^2+λ^2|a̅|^2+4 λ(a̅.c̅) ⇒ 16=4+λ^2+λ ( a̅. c̅=1/4 ) λ ^2+λ 12=0 (λ +4)(λ 3)=0 ⇒λ = 4,3 ...

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Byju's Answer

Standard XII

Mathematics

Condition for Coplanarity of Four Points

Let a , c be ...

Question

Let $\to a, \to c$ be unit vectors and $| \to b | = 4$ . The angle between $\to a$ and $\to c$ is $c o s^{- 1} (\frac{1}{4})$ . Then the positive
integral value of $λ$ . Such that $\to b - 2 \to c = λ \to a$ is ___

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Solution

$(¯ b)^{2} = (2 ¯ c + λ ¯ a)^{2} \Rightarrow | ¯ b |^{2} = 4 | ¯ c |^{2} + λ^{2} | ¯ a |^{2} + 4 λ (¯ a . ¯ c)$
$\Rightarrow 16 = 4 + λ^{2} + λ (¯ a . ¯ c = \frac{1}{4})$
$λ^{2} + λ - 12 = 0$
$(λ + 4) (λ - 3) = 0 \Rightarrow λ = - 4, 3$

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