What is the angle between the following vectors- A -3 -2 -k-B -2 -6 -6 k-cos -112-266cos -1-6-266cos -1-6-1064D- None of these

The correct option is B A.B = (3 × 2) + ( 2 × 6) + (1 × 6) = 6 12 6 = 12 |A| = √(3^2 + ( 2)^2 + 1^2) = √ ...

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Standard XII

Physics

Unit Vectors

What is the a...

Question

What is the angle between the following vectors?

$\to A = 3^i - 2^j +^k$

$\to B = 2^i + 6^j - 6^k$

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None of these

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Solution

The correct option is B

$\to A . \to B = (3 \times 2) + (- 2 \times 6) + (1 \times - 6)$

= 6 - 12 - 6

= -12

$| \to A | = \sqrt{3^{2} + (- 2)^{2} + 1^{2}} = \sqrt{9 + 4 + 1} = \sqrt{14}$

$| \to B | = \sqrt{2^{2} + 6^{2} + (- 6)^{2}} = \sqrt{4 + 36 + 36} = \sqrt{76}$

$\frac{\to A . \to B}{| \to A | | \to B |} = \frac{- 12}{\sqrt{14} \sqrt{76}} = \frac{- 6}{\sqrt{266}}$

$∴ c o s θ = \frac{- 6}{\sqrt{266}}$

$\Rightarrow θ = c o s^{- 1} (\frac{- 6}{\sqrt{266}})$

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Similar questions

What is the angle between the following vectors?

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With respect to a rectangular cartesian coordinate system, three vectors are expressed as $\to a = 4^i -^j, \to b = - 3^i + 2^j$ and
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What is the angle between the following vectors? →A=3^i−2^j+^k →B=2^i+6^j−6^k

The correct option is B →A.→B=(3×2)+(−2×6)+(1×−6) = 6 - 12 - 6 = -12 |→A|=√32+(−2)2+12=√9+4+1=√14 |→B|=√22+62+(−6)2=√4+36+36=√76 →A.→B|→A||→B|=−12√14√76=−6√266 ∴cosθ=−6√266 ⇒θ=cos−1(−6√266)

What is the angle between the following vectors?

$\to A = 3^i - 2^j +^k$

$\to B = 2^i + 6^j - 6^k$