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The cartesian equation of the line barr ...

The cartesian equation of the line `barr = (hati + hatj + hatk)+ lambda(hatj + hatk)` is

A

x=1, y=z

B

`(x-1)/1 = (y-1)/2 = (z-1)/2`

C

x=y=z

D

x-1=y=z

Text Solution

Verified by Experts

The correct Answer is:
A
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Find the angle between the line barr = (hati + 2hatj + hatk) + lambda(hati +hatj + hatk) and the plane barr*(2hati - hatj + hatk) = 5 .

Find the cartesian form of the equation of the plane. barr = (hati + hatj) + s(hati - hatj + 2hatk) + t(hati + 2hatj +hatk) .

Knowledge Check

  • Cartesian form of the eqution of line barr=3hati-5hatj+7hatk+lambda(2hati+hatj-3hatk) is

    A
    `(x-2)/(3)=(y-1)/(-5)=(z+3)/(7)`
    B
    `(x-3)/(2)=(y+5)/(1)=(z-7)/(-3)`
    C
    `(x-2)/(3)=(y-1)/(-5)=(z-3)/(7)`
    D
    `(x-2)/(7)=(y-1)/(-5)=(z+3)/(3)`

  • The shortest distance between the lines vecr = (-hati - hatj) + lambda(2hati - hatk) and vecr = (2hati - hatj) + mu(hati + hatj -hatk) is

    A
    `1/sqrt(7)`
    B
    `1/sqrt(14)`
    C
    `1/(2sqrt(7))`
    D
    `1/(7sqrt(2))`

  • The vector equation of the plane barr=(2hati+hatk)+lamdahati+mu(hati+2hatj-3hatk) is

    A
    `barr.(2hati+3hatj+2hatk)=2`
    B
    `barr.(2hati+3hatj-2hatk)=2`
    C
    `barr.(3hatj+2hatk)=2`
    D
    `barr.(3hatj-2hatk)=2`

    • Similar Questions

    Explore conceptually related problems

    Find the shortest distance betwee the lines : vec(r) = (hati + 2 hatj + hatk ) + lambda ( hati - hatj + hatk) and vec(r) = 2 hati - hatj - hakt + mu (2 hati + hatj + 2 hatk) .

    If the point veca is intersection of the lines vecr = 7 hati + 10hatj + 13 hatk and + lambda ( 2 hati + 3hatj + 4hatk) vecr = 3hati + 5hatj +7 hatk +mu ( hati +2hatj + 3hatk ) then find the value of veca . (2 hati - hatj + hatk) .

    Find the shortest distance between the lines whose vector equations are : vec(r) = (hati + 2 hatj + 3 hatk ) + lambda (hati -3 hatj + 2 hatk) and vec(r) = 4 hati + 5 hatj + 6 hatk + mu (2 hati + 3 hatj + hatk) .

    Find the angle between the line vecr = (hati +2hatj -hatk ) +lambda (hati - hatj +hatk) and vecr cdot (2hati - hatj +hatk) = 4.

    The acute angle between the line barr=(3hati-hatj-hatk)+lambda(hati-hatj+hatk) and the plane barr.(3hati-4hatk)=4 is

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