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The projection of the line segment joini...

The projection of the line segment joining (2,5,6) and (3,2,7) on the line with direction rations 2,1,-2 is

A

`1/2`

B

`1/3`

C

`2`

D

`1`

Text Solution

Verified by Experts

The correct Answer is:
D
The vector joining the points is
`(3-2)hati+(2-5)hatj+(7-6)hatk or hati-3hatj+hatk`
Its projection along the vector `2hati+hatj-2hatk`
`=(|(hati-3hatj+hatk).(2hati+hatj-2hatk)|)/(sqrt(2^2+1^2+2^2))=(|2-3-2|)/3=1`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-THREE DIMENSIONAL GEOMETRY-Exercise 2 (MISCELLANEOUS PROBLEMS)
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  2. If P(0,1,2),Q(4,-2,1) and O(0,0,0) are three points, then /POQ=

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  3. A line makes the same angle theta with each of the x and z-axes. If t...

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  4. If the directions cosines of a vector of magnitude 3 are (2/3,(-a)/3,2...

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  5. If 1/2,1/3,n are direction cosines of a line, then the value of n is

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  6. A line makes an angle theta both with x-axis and y-axis. A possible ra...

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  7. The direction cosines to two lines at right angles are (1,2,3) and (-2...

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  8. A line makes acute angles of alpha,beta and gamma with the coordinate ...

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  9. The direction rations of the diagonals of a cube which joins the origi...

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  10. The projection of the line segment joining (2,5,6) and (3,2,7) on the ...

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  11. In DeltaABC the mid points of the sides AB, BC and CA are (l, 0, 0),...

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  12. The diection cosines of two lines are proportional to (2,3,-6) and (3,...

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  13. The angle between the lines whose direction cosines are (sqrt3/4,1/4,s...

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  14. Let O be the origin and P be the point at a distance 3 units from orig...

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  15. If the points A(2,3,-4), B(1,-2,3) and C(3,lambda,-1) are colliner, th...

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  16. If the directions cosines of a straight line are ltk,k,kgt then

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  17. Find the angle between the following pair of lines: A lines with direc...

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  18. If P(p), Q(q), R(r) and S(s) be four points such that 3p+8q=6r+5s then...

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  19. The direction cosines of line joining (1,-1,1) and (-1,1,1) are

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  20. A vector r is inclined at equal angles to OX,OY and OZ If the magnitud...

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