If a - 2 - 4 - 3 k- - b - - 2 - k- then the scalar product and the angle between them are

Nbsp;a. nbsp;b = a_xb_x + a_yb_y+ a_zb_z a = 2î +4 ĵ+ 3 k̂, nbsp;b = î+ 2ĵ + k̂ a. nbsp;b= 2+8+3 a. nbsp;b=13 nbsp; nbsp;Angle between them is giv ...

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Byju's Answer

Standard XII

Physics

Multiplication with Vectors

If a = 2 î+ 4...

Question

If $\to a = 2^i + 4^j + 3^k, \to b =^i + 2^j +^k,$ then the scalar product and the angle between them are

13, {cos}^{- 1} \frac{13}{\sqrt{174}}

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20, {cos}^{- 1} \frac{20}{\sqrt{184}}

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9, {cos}^{- 1} \frac{13}{\sqrt{174}}

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13, {cos}^{- 1} \frac{29}{\sqrt{174}}

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Solution

The correct option is A $13, {cos}^{- 1} \frac{13}{\sqrt{174}}$
$\to a . \to b = a_{x} b_{x} + a_{y} b_{y} + a_{z} b_{z}$
$\to a = 2^i + 4^j + 3^k, \to b =^i + 2^j +^k$
$\to a . \to b = 2 + 8 + 3 \to a . \to b = 13$

Angle between them is given as
$cos θ = \frac{\to a . \to b}{| \to a | | \to b |} = \frac{13}{\sqrt{29} \sqrt{6}}$
$θ = {cos}^{- 1} \frac{13}{\sqrt{174}}$

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Similar questions

Q. If

\to a = 2^i + 4^j + 3^k, \to b =^i +^j +^k,

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Q. If

\to O P =^i + 4^j - 3^k

and

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Q. I: If

\to a = 3^i - 2^j +^k,

\to b = 2^i - 4^j - 3^k, \to c = -^i + 2^j + 2^k

then

\to a + \to b + \to c = 4^i - 4^j

II: If

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, then magnitude of

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\sqrt{78}

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If →a=2^i+4^j+3^k,→b=^i+2^j+^k, then the scalar product and the angle between them are

The correct option is A 13, cos−113√174→a.→b=axbx+ayby+azbz →a=2^i+4^j+3^k,→b=^i+2^j+^k →a.→b=2+8+3→a.→b=13 Angle between them is given as cosθ=→a.→b|→a||→b|=13√29√6 θ=cos−113√174

If $\to a = 2^i + 4^j + 3^k, \to b =^i + 2^j +^k,$ then the scalar product and the angle between them are