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Show that the position vector of the poi...

Show that the position vector of the point P, which divides the line joining the points A and B having position vectors `veca and vecb` internally in the ratio `m: n" is "(mvecb+nveca)/(m+n)`

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Show that the position vector of the point P, which divides the line joining the points A and B having position vectors veca and vecb internally in ratio m:n is (mvecb+nveca)/(m+n)

Show that the position vector of the point P, which divides the line joining the points A and B having position vector a and b internally in the ratio: m:n is (mvecb + nveca)/(m+n)

Knowledge Check

  • The position vector of the point, which divides the join of the points with position vectors veca + vecb and 2 veca - vecb in the ratio 1:2 is :

    A
    `(3veca + 2 vecb)/( 3)`
    B
    `veca `
    C
    `(5 veca- vecb)/(3)`
    D
    `(4 veca + vecb)/(3).`

  • The position vector of the point, which divides the line segment joining the points (1,3,-9) and (6,-2,-4) in the ratio 2:3 is

    A
    (3,-1,7)
    B
    (-3,1,-7)
    C
    (3,1,-7)
    D
    (-3,-1,7)

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

    A
    j
    B
    i
    C
    k
    D
    `vec 0`

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    Find the position vectors of the points which divide the join of the points 2 vec a-3 vec b a n d 3 vec a-2 vec b internally and externally in the ratio 2:3 .

    Find the coordinates of the point which divides the line joining the points (1,6) and (4,3) in the ratio 1:2 .

    Find the co-ordinates of the point P which divides the line segment joining the points A ( 1, - 2 ,3 ) and B ( 3 , 4 - 5 ) internally in the ratio 2 : 3

    Find the position vector of a point R which divides the line joing two points P and Q whose position vectors are hati+2hatj-hatkand-hati+hatj+hatk repectively , in the ratio 2:1 (i) nternally (ii) externally

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