If a- b- and c- are three unit vectors- no two of which are collinear- a-2 b- is collinear with c- and b-3 c- is collinear with a- then -a-2 b-8 c-A- 2B- 3C- 0D- 6

The correct option is A 2a⃗ + 2b⃗ =λc⃗ . . . (i) b⃗ + 3c⃗ =μa⃗ . . . (ii) (i) 2 × (ii) ⇒a⃗ 6c⃗= λc⃗ 2 μa⃗ ⇒ (1+2μ)a⃗=(6+λ)c⃗ a is not pa ...

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Byju's Answer

Standard XII

Mathematics

Bisector of Angle between Two Vectors

If a⃗, b⃗ and...

Question

If $\to a, \to b a n d \to c$ are three unit vectors, no two of which are collinear, $\to a + 2 \to b$ is collinear with $\to c a n d \to b + 3 \to c$ is collinear with $\to a$ , then $| \to a + 2 \to b + 8 \to c | =$

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Solution

The correct option is A 2
$\to a + 2 \to b = λ \to c$ . . . (i)
$\to b + 3 \to c = μ \to a$ . . . (ii)
(i) - 2 $\times$ (ii) $\Rightarrow \to a - 6 \to c = λ \to c - 2 μ \to a$
$\Rightarrow (1 + 2 μ) \to a = (6 + λ) \to c$
a is not parallel to $\to c \Rightarrow 1 + 2 μ = 0, 6 + λ = 0$
$\Rightarrow μ = - \frac{1}{2}, λ = - 6 p u t t i n g λ = - 6 i n (i) \to a + 2 \to b + 6 \to c = 0 ∴ | \to a + 2 \to b + 6 \to c + 2 \to c | = | 2 \to | = 2$

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