The angle between a- and b- is 5- 6 and the projection of a- on b- is -9 - 3 - then - a- is equal to

The correct option is B 6 Given, angle between a⃗ and b⃗ is 5π #160; 6 and a⃗.b⃗| b⃗| #160; = 9 √( 3 ) #160;[ ∵a⃗.b⃗=| a⃗| | ...

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Byju's Answer

Standard XII

Mathematics

Applications of Dot Product

The angle bet...

Question

The angle between $\to a$ and $\to b$ is $\frac{5 π}{6}$ and the projection of $\to a$ on $\to b$ is $\frac{- 9}{\sqrt{3}}$ , then $| \to a |$ is equal to

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Solution

The correct option is B $6$
Given, angle between $\to a$ and $\to b$ is $\frac{5 π}{6}$
and $\frac{\to a . \to b}{∣ ∣ \to b ∣ ∣} = \frac{- 9}{\sqrt{3}} [∵ \to a . \to b = | \to a | ∣ ∣ \to b ∣ ∣ cos θ]$
$\Rightarrow | \to a | cos θ = \frac{- 9}{\sqrt{3}}$
$\Rightarrow | \to a | \times cos \frac{5 π}{6} = \frac{- 9}{\sqrt{3}} \Rightarrow | \to a | = 6$

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Similar questions

Q. If the projection of

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and the projection of

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\to a

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Q. If

\to a, \to b

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and

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respectively and if

| \to a + \to b | = 6, | \to b + \to c | = 8

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Q. If

| \to a | = 8, | \to b | = 3

and

| \to a \times \to b | = 12

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The angle between →a and →b is 5π6 and the projection of →a on →b is −9√3, then |→a| is equal to

The correct option is B 6Given, angle between →a and →b is 5π6and →a.→b∣∣→b∣∣=−9√3[∵→a.→b=|→a|∣∣→b∣∣cosθ]⇒|→a|cosθ=−9√3⇒|→a|×cos5π6=−9√3⇒|→a|=6

The angle between $\to a$ and $\to b$ is $\frac{5 π}{6}$ and the projection of $\to a$ on $\to b$ is $\frac{- 9}{\sqrt{3}}$ , then $| \to a |$ is equal to