The acute angle between two lines r -2 -5 -k-3 -2 -6 k- and r -7 -6 -k-2 -2 k- i-A- cos -117-21B- cos -119-21C- cos -14-22D- cos -113-22

The correct option is B cos θ=(3 î+2ĵ+6k̂).(î+2ĵ+2̂k)/ | 3î+ 2ĵ+6k̂ |. | î+ 2ĵ+2k̂ |=3+4+12/7 × 3=19/21 θ = cos^ 1 ( 19/21 ) ...

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Multiplication with Vectors

The acute ang...

Question

The acute angle between two lines $\to r = 2^i - 5^j +^k + α (3^i + 2^j + 6^k) a n d \to r = 7^i - 6^j +^k + β (^i + 2^j + 2^k)$ is

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Solution

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

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

Find the angle between the following pairs of lines :

$r = 2^i - 5^j +^k + λ (3^i + 2^j + 6^k) a n d r = 7^i - 6^k + μ (^i + 2^j + 2^k)$

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

{\to r}_{1} =^i + 6^j + 4^k + λ (2^i -^j + 3^k)

{\to r}_{2} = 4^i + 2^j -^k + λ (^i + 2^j -^k)

(a) {sin}^{- 1} (\frac{3}{2 \sqrt{21}}) (b) {cos}^{- 1} (\frac{3}{2 \sqrt{21}})

(c) - {sin}^{- 1} (\frac{3}{2 \sqrt{21}}) (d) - {cos}^{- 1} (\frac{3}{2 \sqrt{21}})

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

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

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

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

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

\to r (4^i + 5^j + 6^k) + μ (2^i + 3^j +^k)

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