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If the position vectors of the points A and B respectively are i+2j-3k and j-k find the direction cosines of AB

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The position vector of a point C with respect to B is hat i +hat j and that of B with respect to A is hati-hatj . The position vector of C with respect to A is

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Knowledge Check

  • If the position vectors of the points A and B are 3i+j+2k and i-2 j-4k respectively, then the equation of the plane through B and perpendicular to AB is

    A
    2x+3y+6z+28 =0
    B
    3x+2y+6z+28
    C
    2x-3y+6z+28 =0
    D
    3x-2y+6z =28

  • The position vectors of the vertices of a triangle are 2i-j+k, i-3j-5k and 3i-4j-4k then it is

    A
    equilateral triangle
    B
    isosceles triangle
    C
    right anglesioscles triangle
    D
    right angled triangle

  • If the position vectors of A and B are 3i-2j+k and 2i+4j+3k then |vec AB| =

    A
    `sqrt41`
    B
    `sqrt29`
    C
    `sqrt43`
    D
    `sqrt53`

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    Find the position vectors of a point R which divides the line joining two points P and Q whose position vectors are hat(i)+2hat(j)-hat(k)- and - hat(i)+hat(j)-hat(k) respectively, in the ration 2:1 . (i) Internally, (ii) Externally.

    The values of 'a' for which the points A, B, C with position vectors 2i-j+k, i-3j-5k and ai-3j+k respectively are the vertices of a right angled triangle with C = pi/2 are

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    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

    The three points whose position vectors are i+2j+3k, 3i+4j+7k, and -3i-2j-5k

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