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- 2y-a-b-21 - 2- then the value of - isA- 5B- 25- 125D- 625

The correct option is D 625|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^2 ...

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Byju's Answer

Standard XII

Mathematics

Cross Product of Two Vectors

Let a⃗ and b⃗...

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

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Q. If

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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