Let a- and b- be unit vectors such that -a-b-3- Then the value of 2a-5b- 3a-b-a-b- is

The correct option is B 392 |a⃗ +b⃗|=√(3) 1+1+2(a⃗.b⃗)=3 a⃗.b⃗=12 (2a⃗+5b⃗)(3a⃗+b⃗+a⃗×b⃗) nbsp; =6+5+2(a⃗.b⃗)+15(b⃗.a⃗) = ...

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Byju's Answer

Standard XII

Mathematics

AM,GM,HM Inequality

Let a⃗ and ...

Question

Let $\to a$ and $\to b$ be unit vectors such that $| \to a + \to b | = \sqrt{3}$ . Then the value of $(2 \to a + 5 \to b) \cdot (3 \to a + \to b + \to a \times \to b)$ is

39

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\frac{39}{2}

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\frac{35}{7}

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None of these

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Solution

The correct option is B $\frac{39}{2}$
$| \to a + \to b | = \sqrt{3}$
$⟹ 1 + 1 + 2 (\to a . \to b) = 3$
$⟹ \to a . \to b = \frac{1}{2}$
$(2 \to a + 5 \to b) (3 \to a + \to b + \to a \times \to b)$ $= 6 + 5 + 2 (\to a . \to b) + 15 (\to b . \to a)$
$= 11 + 17 \times \frac{1}{2}$
$= \frac{39}{2}$

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Similar questions

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Let →a and →b be unit vectors such that |→a+→b|=√3. Then the value of (2→a+5→b)⋅(3→a+→b+→a×→b) is

The correct option is B 392|→a+→b|=√3⟹1+1+2(→a.→b)=3⟹→a.→b=12(2→a+5→b)(3→a+→b+→a×→b) =6+5+2(→a.→b)+15(→b.→a)=11+17×12=392

Let $\to a$ and $\to b$ be unit vectors such that $| \to a + \to b | = \sqrt{3}$ . Then the value of $(2 \to a + 5 \to b) \cdot (3 \to a + \to b + \to a \times \to b)$ is

The correct option is B $\frac{39}{2}$
$| \to a + \to b | = \sqrt{3}$
$⟹ 1 + 1 + 2 (\to a . \to b) = 3$
$⟹ \to a . \to b = \frac{1}{2}$
$(2 \to a + 5 \to b) (3 \to a + \to b + \to a \times \to b)$ $= 6 + 5 + 2 (\to a . \to b) + 15 (\to b . \to a)$
$= 11 + 17 \times \frac{1}{2}$
$= \frac{39}{2}$