If a-10- b-2 and a-b-12- then the value of -a-b- isa 5 b 10 c 14 d 16

(d) Here,a=10,b=2 and a.b=12 [given] ∴ a.b=|a||b|cos θ 12=10×2cosθ ⇒ cos θ=12/20=3/5 ⇒ sin θ=√(1 cos^2 θ)=√(1 9/25) sin θ=± 4/5 ∴ ...

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Standard XII

Mathematics

Implicit Differentiation

If a⃗=10, b⃗=...

Question

If $\to a = 10, \to b = 2 a n d \to a . \to b = 12, t h e n t h e v a l u e o f | \to a \times \to b |$ is

(a) 5 (b) 10 (c) 14 (d) 16

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Solution

(d) Here, $\to a = 10, \to b = 2 a n d \to a . \to b = 12 [g i v e n] ∴ \to a . \to b = | \to a | | \to b | c o s θ 12 = 10 \times 2 c o s θ \Rightarrow c o s θ = \frac{12}{20} = \frac{3}{5} \Rightarrow s i n θ = \sqrt{1 - c o s^{2} θ} = \sqrt{1 - \frac{9}{25}} s i n θ = \pm \frac{4}{5} ∴ | \to a \times \to b | = | \to a | | \to b | s i n θ | = 10 \times 2 \times \frac{4}{5} = 16$

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If →a=10,→b=2 and →a.→b=12,then the value of |→a×→b| is (a) 5 (b) 10 (c) 14 (d) 16

(d) Here,→a=10,→b=2 and →a.→b=12 [given]∴ →a.→b=|→a||→b|cosθ12=10×2cosθ⇒ cosθ=1220=35⇒ sinθ=√1−cos2θ=√1−925sinθ=± 45∴ |→a×→b|=|→a||→b|sinθ|=10×2×45=16

If $\to a = 10, \to b = 2 a n d \to a . \to b = 12, t h e n t h e v a l u e o f | \to a \times \to b |$ is

(a) 5 (b) 10 (c) 14 (d) 16