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If a line in the space passes through th...

If a line in the space passes through the points `(x_(1),y_(1),z_(1))` and `(x_(2),y_(2),z_(2))` then its direction consines are proportional to

A

`x_(1)x_(2), y_(1)y_(2), z_(1),z_(2)`

B

`x_(1)^(2) -x_(2)^(2), y_(1)^(2) - y_(2)^(2), z_(1)^(2) -z_(2)^(2)`

C

`x_(1) + x_(2), y_(1) +y_(2), z_(1) +z_(2)`

D

`x_(1)-x_(2), y_(1)-y_(2), z_(1)-z_(2)`

Text Solution

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The correct Answer is:
D
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Knowledge Check

  • Equation of plane passing through (x_(1),y_(1),z_(1)),(x_(2),y_(2),z_(2)) and the origin is

    A
    `|{:(1,x,x_(1)-x_(2)),(1,y,y_(1)-y_(2)),(1,z,x_(1)-z_(2)):}|=0`
    B
    `|{:(x,y,z),(x_(1),y_(1),z_(1)),(x_(2),y_(2),z_(2)):}|=0`
    C
    `|{:(x-x_(1),y-y_(1),z-z_(1)),(x_(1)-x_(2),y_(1)-y_(2),z_(1)-z_(2)),(1,1,1):}|=0`
    D
    `|{:(1,x,x_(1)),(1,y,y_(1)),(1,z,z_(1)):}|=0`

  • If planes are drawn parallel to the coordinate planes through the points P(x_(1),y_(1),z_(1)) and Q(x_(2),y_(2),z_(2)) then the lengths of the eges of the parallelopied formed are

    A
    `x_(2)-x_(1),y_(2)-y_(1),z_(2)-z_(1)`
    B
    `x_(2)+x_(1),y_(2)+y_(1),z_(2)+z_(1)`
    C
    `x_(1)x_(2),y_(1)y_(2),z_(1)z_(2)`
    D
    none of these

  • Distance of the point (x_(1),y_(1),z_(1)) from the line (x-x_(2))/1=(y-y_(2))/m=(z-z_(2))/n where l,m,n are direction cosines of the line, is

    A
    `[(x_(1)-x_(2))^(z)+(y_(2)-y_(1))^(2)+(z_(1)+z_(2))^(2)-{l(x_(1)-x_(2))+m(y_(1)-y_(2))+n(z_(1)-z_(2))}^(2)]^(2//1)`
    B
    `sqrt((x_(2)-x_(1))^(2)+(y_(2)_y_(1))^(2)+(z_(2)-z_(1))^(2))`
    C
    `sqrt((x_(2)-x_(1))l+(y_(2)-y_(1))m+(z_(2)-z_(1))n)`
    D
    none of these

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