Then - ivec u timesivec v-1

The correct option is A 2 √(16 (a⃗.b⃗)^2) |u⃗×v⃗| =|(a⃗ b⃗)×(a⃗+b⃗)| =|2a⃗×b⃗| =2 |a⃗| |b⃗| sin θ =8 sin θ = 8 √(1 cos^2 θ) = 8 √(1 (a⃗.b⃗4 )^2) (∵a ...

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Byju's Answer

Standard IX

Mathematics

Cross Product of Two Vectors

then | ivec u...

Question

$I f \to u = \to a - \to b a n d \to v = \to a + \to b a n d | \to a | = | \to b | = 2, t h e n | \to u \times \to v | =$

$2 \sqrt{16 - (\to a . \to b)^{2}}$

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$\sqrt{16 - (\to a . \to b)^{2}}$

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$2 \sqrt{4 - (\to a . \to b)^{2}}$

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$\sqrt{4 - (\to a . \to b)^{2}}$

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Solution

The correct option is A
$2 \sqrt{16 - (\to a . \to b)^{2}}$

$| \to u \times \to v | = | (\to a - \to b) \times (\to a + \to b) | = | 2 \to a \times \to b | = 2 | \to a | | \to b | s i n θ = 8 s i n θ = 8 \sqrt{1 - c o s^{2} θ} = 8 \sqrt{1 - {(\frac{\to a . \to b}{4})}^{2}} (∵ \to a . \to b = 4 c o s θ) = 2 \sqrt{16 - (\to a . \to b)^{2}}$

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Q. Match the following:

\begin{matrix} Column I & Column II (a) & If the vectors \to a, \to b, \to c form sides - - \to B A, - - \to C A, & (p) & \to a . \to c = \to b . \to c = \to c . \to a - - \to C B of Δ A B C, then (b) & If \to a, \to b, \to c are forming three adjacent sides of & (q) & \to a . \to b = \to b . \to c = \to c . \to a = 0 regular tetrahedron, then (c) & If \to a \times \to b = \to c and \to b \times \to c = \to a then & (r) & \to a \times \to b = \to b \times \to c = \to c \times \to a (d) & \to a, \to b, \to c are unit vectors and \to a + \to b + \to c = 0 then & (s) & \to a . \to b + \to b . \to c + \to c . \to a = - \frac{3}{2} \end{matrix}

If $| u | < 1, | v | < 1$ , and $z = \frac{u - v}{1 + ¯ u v}$ , then least value of $| z |$ is

Q. If

| u | = | v | = 1, u v \neq - 1,

and

z = \frac{u - v}{1 + u v}

, then

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If →u=→a−→b and →v=→a+→b and |→a|=|→b|=2, then |→u×→v|=

The correct option is A 2√16−(→a.→b)2 |→u×→v|=|(→a−→b)×(→a+→b)|=|2→a×→b|=2 |→a||→b| sin θ=8 sin θ=8√1−cos2 θ=8√1−(→a.→b4)2 (∵→a.→b=4 cos θ)=2√16−(→a.→b)2

$I f \to u = \to a - \to b a n d \to v = \to a + \to b a n d | \to a | = | \to b | = 2, t h e n | \to u \times \to v | =$