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Find the position vector of the point wh...

Find the position vector of the point which divides the line joining the points `bar(i)+bar(j)-4bar(k) and bar(i)+bar(j)+bar(k)` in the ratio 3 : 2.

A

i+j-k

B

i-j+k

C

i-j-k

D

i+j+k

Text Solution

Verified by Experts

The correct Answer is:
`bar(i)+bar(j)-bar(k)`
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Explore conceptually related problems

Find the position vector of the point which divides the line joining the points 3bar(a)-4bar(b) and 4bar(a)-3bar(b) in the ratio 2 : 3 (i) internally and (ii) externally.

Find the vector equation of the line joining the points 2bar(i)+bar(j)+3bar(k) and -4bar(i)+3bar(j)-bar(k) .

Knowledge Check

  • The vector equation of the line joining the points 3bar(i)+2bar(j)-4bar(k), 5bar(i)+4bar(j)-6bar(k) is

    A
    `bar(r)=(3bar(i)+2bar(j)-4bar(k))+t(2bar(i)+2bar(j)-2bar(k))`
    B
    `bar(r)=(3bar(i)+2bar(j)-4bar(k))+t(2bar(i)-2bar(j)+2bar(k))`
    C
    `bar(r)=(3bar(i)+2bar(j)-4bar(k))+t(-2bar(i)+2bar(j)-2bar(k))`
    D
    `bar(r)=(5bar(i)+4bar(j)-6bar(k))+t(3bar(i)+2bar(j)-4bar(k))`

  • The position vector of a point lying on the line joining the points whose position vectors are bar(i)+bar(j)-bar(k) and bar(i)-bar(j)+bar(k) is

    A
    `bar(j)`
    B
    `bar(i)`
    C
    `bar(k)`
    D
    `bar(0)`

  • The equation to the line passing through the points A(bar(i)+bar(j)+bar(k)) and B(bar(i)+bar(j)-bar(k)) is

    A
    `bar(r)=bar(i)+(1+t)bar(j)+(1-2t)bar(k)`
    B
    `bar(r)=(1+t)bar(i)+bar(j)(1-2t)bar(k)`
    C
    `bar(r)=bar(i)+bar(j)+(1-2t)bar(k)`
    D
    `bar(r)=bar(i)-2bar(j)+tbar(k)`

    • Similar Questions

    Explore conceptually related problems

    Find the vector equation of the line joining the point 2 bar(i) + bar(j) + 3 bar(k) and - 4 bar(i) + 3 bar(j) - bar(k)

    Find the vector equation of the line passing through the points bar(i)+bar(j)+bar(k) and bar(i)-bar(j)+bar(k) .

    Find the vector equation of the line passing through the points 2 bar(i)+bar(j)+3bar(k) and -4bar(i)+3bar(j)-bar(k) .

    Find the vector equation of the plane which passes through the points 2 bar(i)+ 4 bar(j) + 2 bar(k), 2 bar(i) + 3 bar(j) + 5 bar(k) and parallel to the vector 3 bar(i) - 2 bar(j) + bar(k) . Also find the point where this plane meets the line joining the points 2 bar(i) + bar(j) + 3 bar(k) and 4 bar(i) - 2 bar(j) + 3 bar(k)

    Find the direction cosines of the line joining the points with position vectors -bar(i)+bar(j)+bar(k), 2bar(i)+3bar(j)-5bar(k) .

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