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Find the angle between the lines vecr = ...

Find the angle between the lines `vecr = (hati+hatj)+lambda(3hati+2hatj+6hatk)` and `vecr = (hati-hatk) + mu(hati+2hatj+2hatk)`

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Here `vecm = 3hati+2hatj+6hatk` and `vecn=hati+2hatj+2hatk`
Let ` theta` be the angle between two lines .
`:. cos theta = (vecm.vecn)/(|vecm||vecn|) = ((3hati+2hatj+6hatk).(hati+2hatj+2hatk))/(|3hati+2hatj+6hatk|| hati+2hatj+2hatk|)`
`= (3+4+12)/(sqrt(9+4+36)sqrt(1+4+4)) = (19)/(7xx3) = (19)/(21)`
`theta = cos^(-1) (19/21)`
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NAGEEN PRAKASHAN-THREE-DIMENSIONAL GEOMETRY -Miscellaneous Exercise
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  6. If the coordinates of the points A,B,C,D be 91,2,3),(4,5,7),(-4,3,-6) ...

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  7. If the lines (x-1)/(-3)=(y-2)/(2k)=(z-3)/2and (x-1)/(3k)=(y-1)/1=(z-6...

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  8. Find the vector equation of the line passing through (1, 2, 3) and ...

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  9. Find the equation of the plane passing through (a,b,c) and paralle tot...

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  10. Find the shortest distance between lines vecr = 6hati+2hatj+2hatk+la...

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  11. Find the coordinates of the point where the line through (5, 1, 6) ...

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  12. Find the coordinates of the point where the line through (5, 1, 6) ...

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  13. find the coordinates of point where the line through (3,-4,-5) and (2,...

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  14. Find the equation of the plane passing through the point (-1, 3, 2) an...

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  15. If the points (1," "1," "p)" "a n d" "(" "3," "0," "1) be equidistant ...

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  16. Find the equation of the plane passing through the line of intersectio...

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  17. If O be the origin and the coordinates of P be (1,2,-3) then find the ...

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  18. Find the equation of the plane which contains the line of intersection...

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  19. Find the distance of the point (-1,-5,-10) from the point of the inter...

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  20. Find the vector equation o the line passing through (1,2,3) and parall...

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  21. Find the vector equation of the line passing through the point (1,2,4)...

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