The angle between the planes r-2-2k-3 and r-3-6-2k-4Cos-1-16-21 -Sin-1-4-21 -Cos-1-1-4 -Cos-1-3-4 -

The correct option is A Cos^ 1(16/21 )Let a =2î ĵ=2k̂, b=3î 6ĵ+2k̂ If θ is the angle between the planes then cos θ =cos(a,b)=ab/|a||b|=6+6+4/√(4+1+4)√(9+36+4) ...

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Standard XII

Mathematics

Angle between Two Planes

The angle bet...

Question

The angle between the planes $r . (2^i -^j + 2^k) = 3$ and $r . (3^i - 6^j + 2^k) = 4$

C o s^{- 1} (\frac{16}{21})

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S i n^{- 1} (\frac{4}{21})

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C o s^{- 1} (\frac{1}{4})

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C o s^{- 1} (\frac{3}{4})

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Solution

The correct option is A $C o s^{- 1} (\frac{16}{21})$
Let $a = 2^i -^j = 2^k, b = 3^i - 6^j + 2^k$
If $θ$ is the angle between the planes then
$c o s θ = c o s (a, b) = \frac{a b}{| a | | b |} = \frac{6 + 6 + 4}{\sqrt{4 + 1 + 4} \sqrt{9 + 36 + 4}} = \frac{16}{3 \times 7} = \frac{16}{21}$

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Similar questions

Q. Find the angle between the following pair of lines:
(i)

\to r = 2^i - 5^j +^k + λ (3^i - 2^j + 6^k)

and

\to r = 7^i - 6^k + μ (^i + 2^j + 2^k)

(ii)

\to r = 3^i +^j - 2^k + λ (^i -^j - 2^k)

and

\to r = 2^i -^j - 56^k + μ (^3 i - 5^j - 4^k)

Q. The angle between the planes

r . (2^i -^j + 2^k) = 3

and

r . (3^i - 6^j + 2^k) = 4

Q. The angle between the planes

r . (2^i -^j + 2^k) = 3

and

r . (3^i - 6^j + 2^k) = 4

Q. Find the angle between the following pairs of lines :

r = 3^i +^j - 2^k + λ (^i -^j - 2^k) a n d r = 2^i -^j - 56^k + μ (3^i - 5^j - 4^k)

Q. Find the angle between the pair of lines given by
i)

\to r = 2^i - 5^j +^k + λ (3^i + 2^j + 6^k)

and

\to r = 7^i - 6^k + μ (^i + 2^j + 2^k)

ii)

\to r = 3^i +^j - 2^k + λ (^i -^j - 2^k)

and

\to r = 2^i -^j - 56^k + μ (3^i - 5^j - 4^k)

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The angle between the planes r.(2^i−^j+2^k)=3 and r.(3^i−6^j+2^k)=4

The correct option is A Cos−1(1621)Let a=2^i−^j=2^k,b=3^i−6^j+2^k If θ is the angle between the planes then cosθ=cos(a,b)=ab|a||b|=6+6+4√4+1+4√9+36+4=163×7=1621

The angle between the planes $r . (2^i -^j + 2^k) = 3$ and $r . (3^i - 6^j + 2^k) = 4$

The correct option is A $C o s^{- 1} (\frac{16}{21})$
Let $a = 2^i -^j = 2^k, b = 3^i - 6^j + 2^k$
If $θ$ is the angle between the planes then
$c o s θ = c o s (a, b) = \frac{a b}{| a | | b |} = \frac{6 + 6 + 4}{\sqrt{4 + 1 + 4} \sqrt{9 + 36 + 4}} = \frac{16}{3 \times 7} = \frac{16}{21}$