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A point on a line has coordinates (p+1,p...

A point on a line has coordinates `(p+1,p-3,sqrt2p)` where p is any number. What are direction cosines of the line

A

`1/2,1/2,1/sqrt2`

B

`1/sqrt2,1/2,1/2`

C

`1/sqrt2,1/2,-1/2`

D

cannot be determined due to insufficient data

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • If P is (-1,1,2) , then direction cosines of line OP are

    A
    `(-1)/2,1/2,1`
    B
    `(-1)/(sqrt(6)),1/(sqrt(6)),(2)/(sqrt(6))`
    C
    `1/(sqrt(6)),(-1)/(sqrt(6)),2/(sqrt(3))`
    D
    `-1,1,2`

  • If P-=(1,2,3) then direction cosines of OP are

    A
    `1,2,3`
    B
    `-1,-2,-3`
    C
    `(1)/(sqrt(14)),(2)/(sqrt(14)),(3)/(sqrt(14))`
    D
    `(-1)/(sqrt(14)),(2)/(sqrt(14)),(3)/(sqrt(14))`

  • If P(x,y,z) is a point in space at a distance r from the origin O, then the direction cosines of the line OP are

    A
    `(r)/(x),(r)/(y),(r)/(z)`
    B
    `rx,ry,rz`
    C
    `(x)/(r),(y)/(r),(z)/(r)`
    D
    `r^(2)x,r^(2)y,r^(2)z`

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