Let V be a unit vector which follows the equation v - b - c- Also- - b -2 and - c -3 then v - x b - y b - c- then the value2 x - y is

B× (v×b)=b×c 4 v (b.v)b=b×c |v×b|=|c| ⇒ |v||b|sin θ=|c| 2|v|sin θ=√(3)⇒sin θ=√(3)/2, cos θ=1/2 ⇒ 4v ( 2 × 1 ×1/2 )b=b×c v=1/4(b+b×c) x=1/4, y=1/4 ...

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Byju's Answer

Standard XII

Mathematics

Multiplication of Matrices

Let V be a un...

Question

Let $\to v$ be a unit vector which follows the equation $\to v \times \to b = \to c$ . Also, $| \to b | = 2$ and $| \to c | = \sqrt{3}$ then $\to v = x \to b + y \to b \times \to c$ , then the value $2 (x + y)$ is

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Solution

$\to b \times (\to v \times \to b) = \to b \times \to c$

$4 \to v - (\to b . \to v) \to b = \to b \times \to c$

$| \to v \times \to b | = | \to c |$

$\Rightarrow | \to v | | \to b | sin θ = | \to c |$

$2 | \to v | sin θ = \sqrt{3} \Rightarrow sin θ = \frac{\sqrt{3}}{2}, cos θ = \frac{1}{2}$

$\Rightarrow 4 \to v - (2 \times 1 \times \frac{1}{2}) \to b = \to b \times \to c$

$\to v = \frac{1}{4} (\to b + \to b \times \to c)$

$x = \frac{1}{4}, y = \frac{1}{4}$

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Let →v be a unit vector which follows the equation →v×→b=→c. Also, |→b|=2 and |→c|=√3 then →v=x→b+y→b×→c, then the value 2(x+y) is

→b×(→v×→b)=→b×→c 4→v−(→b.→v)→b=→b×→c |→v×→b|=|→c| ⇒|→v||→b|sin θ=|→c| 2|→v|sin θ=√3⇒sin θ=√32, cos θ=12 ⇒4→v−(2×1×12)→b=→b×→c →v=14(→b+→b×→c) x=14, y=14

Let $\to v$ be a unit vector which follows the equation $\to v \times \to b = \to c$ . Also, $| \to b | = 2$ and $| \to c | = \sqrt{3}$ then $\to v = x \to b + y \to b \times \to c$ , then the value $2 (x + y)$ is