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The cartestian equation of a line is `(x-5)/3=(y+4)/7=(z-6)/2`. Write its vector form.

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The correct Answer is:
The cartestian co-ordiates of a point on the given line are (5, -4, 6). Its position vector is `veca=5hati-4hatj+6hatk`. The direction ratios of the line are 3, , 2
`therefore` A vector parallel to the given line is `vecb=3hati+7htj+2hatk`
Hence, the vector equation of the line is `ver=5hati-4hatj+6hatk+lambda(3hati+7hatj+2hatk)`
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A N EXCEL PUBLICATION-THREE DIMENSTIONAL GEOMETRY-QUESTION BANK
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  4. Find the vector and the cartesian equation of the lines that passes th...

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  5. Find the vector and the cartesian equations of the lines that passes t...

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

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

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

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

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

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

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

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

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