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Find the angles between the lines (x-2...

Find the angles between the lines
`(x-2)/2=(y-1)/5=(z+3)/-3` and `(x+2)/-1=(y-4)/8=(z-5)/4`

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The correct Answer is:
The direction ratios of the two lines are respectively 2, 5, -3 and -1, 8, 4
`therefore costheta=(a_1a_2+b_1b_2+c_1c_2)/(sqrt(a_1^2+b_1^2+c_1^2)sqrt(a_2^2+b_2^2+c_2^2)) = (2xx(1)+5xx8+(-3)xx4)/(sqrt(4+25+9)sqrt(1+64+16)) = (-2+40-12)/(sqrt38sqrt81) = (26)/(9sqrt36) rArrtheta = cos^(-)(26/(9sqrt38))`
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A N EXCEL PUBLICATION-THREE DIMENSTIONAL GEOMETRY-QUESTION BANK
  1. Find the angle between the pair lines barr=2i-5j+k+lambda(3i+2j+6k) ...

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  2. Find the angle between the following pairs of lines.vecr = 3hati+hatj-...

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  3. Find the angles between the lines (x-2)/2=(y-1)/5=(z+3)/-3 and (x+...

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  4. Find the angle between the following pairs of lines.(x)/2=(y)/2=(z)/1 ...

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  5. Find the values of p so that the lines (1-x)/3 = (7y-14)/(2p) = (z-3)/...

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  6. Find the shortest distance between the lines whose vector equations ...

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  7. Find the shortest distance between the lines vecr = (1-t)hati+(t-2)hat...

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  8. Consider the plane passing through (2, 3, 5) and perpendiular to the v...

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  9. Consider the plane passing through (2, 3, 5) and perpendiular to the v...

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  10. Consider a plane passing through the points A(-2, 6, -6), B(-3, 10, -9...

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  11. Consider a plane passing through the points A(-2, 6, -6), B(-3, 10, -9...

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  12. Find the eqauation of the plane through the points (2, 1, -1) and (-1,...

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  13. Consider the points A(2, 2, 1) and B(9, 3, 6) and the plane 2x+6y+6z-1...

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  14. Find the equation of the plane that contains the point (1, -1, 2) and ...

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  15. Suppose that a plane meets the co-ordinate axes at A, B, C such that t...

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  16. Find the vector equation of the plane passing through the intersection...

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  17. Consider a point P(-2, -1, -4) and the plane vecr.(3hati+4hatj+5hatk)=...

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  18. Consider a point P(-2, -1, -4) and the plane vecr.(3hati+4hatj+5hatk)=...

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  19. Consider the line (x-1)/2 = (y-2)/-3=(z+5)/4 and the plane 2x+4y-z=3. ...

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  20. Consider the line vecr = (hati+2hatj-hatk)+lambda(2hati+hatj+4hatk) an...

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