Let a and b be two vectors of equal magnitude 5 uints- Let p- q be vectors such that p-a-b and q-a-b- If -p-q-2-a-b21-2- then the value of - is

|p× nbsp;q| = 2{γ (a.b)^2}^1/2⋯(1) p× nbsp;q=(a b)× (a+b) ⇒p× nbsp;q=2(a×b) ⇒p× nbsp;q=2|a|| b|sinθ ⇒p× nbsp;q=50√(1 cos^2θ) ⇒p× nbsp;q=2√(625 625co ...

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Byju's Answer

Standard XII

Mathematics

Cross Product of Two Vectors

Let a and b b...

Question

Let $\to a$ and $\to b$ be two vectors of equal magnitude $5$ uints. Let $\to p, \to q$ be vectors such that $\to p = \to a - \to b$ and $\to q = \to a + \to b$ . If $| \to p \times \to q | = 2 {γ - (\to a . \to b)^{2}}^{1 / 2}$ , then the value of $γ$ is

5

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25

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125

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625

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Solution

The correct option is D $625$
$| \to p \times \to q | = 2 {γ - (\to a . \to b)^{2}}^{1 / 2} \dots (1)$
$\to p \times \to q = (\to a - \to b) \times (\to a + \to b)$
$\Rightarrow \to p \times \to q = 2 (\to a \times \to b)$
$\Rightarrow \to p \times \to q = 2 | \to a | | \to b | sin θ$
$\Rightarrow \to p \times \to q = 50 \sqrt{1 - {cos}^{2} θ} \Rightarrow \to p \times \to q = 2 \sqrt{625 - 625 {cos}^{2} θ}$

We know that,
$\to a \cdot \to b = | \to a | | \to b | cos θ = 25 cos θ$

Using the equation (1),
$2 \sqrt{625 - 625 {cos}^{2} θ} = 2 {γ - (\to a . \to b)^{2}}^{1 / 2} \Rightarrow 2 \sqrt{625 - 625 {cos}^{2} θ} = 2 {γ - 625 {cos}^{2} θ}^{1 / 2}$
$\Rightarrow γ = 625$

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Similar questions

Q. Let

\to a

and

\to b

be two vectors of equal magnitude

5

uints. Let

\to p, \to q

be vectors such that

\to p = \to a - \to b

and

\to q = \to a + \to b

. If

| \to p \times \to q | = 2 {γ - (\to a . \to b)^{2}}^{1 / 2}

, then the value of

γ

Q. Let

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and

c

be three non-coplanar vectors and let

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and

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and

r = \frac{a \times b}{a b c}

Then the value of the expression

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is equal to

Q. Let

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c

be three non-coplanar vectors, and let

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r

be the vectors defined by the relation

p = \frac{b \times c}{[a b c]}, q = \frac{c \times a}{[a b c]},

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Q. Let

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be two vectors. If a vector

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then

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Let →a and →b be two vectors of equal magnitude 5 uints. Let →p, →q be vectors such that →p=→a−→b and →q=→a+→b. If |→p×→q|=2{γ−(→a.→b)2}1/2, then the value of γ is

Let $\to a$ and $\to b$ be two vectors of equal magnitude $5$ uints. Let $\to p, \to q$ be vectors such that $\to p = \to a - \to b$ and $\to q = \to a + \to b$ . If $| \to p \times \to q | = 2 {γ - (\to a . \to b)^{2}}^{1 / 2}$ , then the value of $γ$ is