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प्रश्न
The angle between the lines `barr = (hati+2hatj - 3hatk) + λ(3hati+2hatj+6hatk) and barr = (5hati-2hatj+7hatk) +μ(hati+2hatj+2hatk)` is ______.
पर्याय
`cos^-1 (17/21)`
`cos^-1 (20/21)`
`cos^-1 (18/21)`
`cos^-1 (19/21)`
MCQ
रिकाम्या जागा भरा
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उत्तर
The angle between the lines `barr = (hati+2hatj - 3hatk) + λ(3hati+2hatj+6hatk) and barr = (5hati-2hatj+7hatk) +μ(hati+2hatj+2hatk)` is `\underlinebb(cos^-1 (19/21))`.
Explanation:
`costheta = (veca.vecb)/(|veca| |vecb|)`
`veca.vecb = (3)(1)+(2)(2)+(6)(2)=3+4+12=19`
`|veca|=sqrt(3^2+2^2+6^2) = sqrt(9+4+36) = sqrt49 = 7`
`|vecb| = sqrt(1^2+2^2+2^2) = sqrt(1+4+4) = sqrt9 = 3`
`costheta = 19/(7xx3) = 19/21`
`theta = cos^-1 (19/21)`
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