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Points A and B have position vector vec(...

Points A and B have position vector `vec(a)=-3hat(i)+2hat(j)+7hat(k)` and `vec(b)=3hat(i)+4hat(j)-5hat(k)` respectively. Find : `|vec(AB)|`

Text Solution

Verified by Experts

The correct Answer is:
`sqrt(184)`
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Points A and B have position vector vec(a)=-3hat(i)+2hat(j)+7hat(k) and vec(b)=3hat(i)+4hat(j)-5hat(k) respectively. Find : vec(AB)

Points A and B have position vector vec(a)=-3hat(i)+2hat(j)+7hat(k) and vec(b)=3hat(i)+4hat(j)-5hat(k) respectively. Find : The direction cosines l, m, n of vec(AB)

Knowledge Check

  • If the position vectors of the points P and Q are 2hat(i)+hat(k) " and " -3hat(i)-4hat(j)-5hat(k) respectively, then vector vec(OP) is -

    A
    `5hat(i)+4hat(j)+4hat(k)`
    B
    `5hat(i)+4hat(j)+6hat(k)`
    C
    `5hat(i)-4hat(j)+4hat(k)`
    D
    `-hat(i)-4hat(j)-4hat(k)`

  • The lines vec(r)=hat(i)+t(5hat(i)+2hat(j)+hat(k)) and vec(r)=hat(i)+s(-10hat(i)-4hat(j)-2hat(k)) are -

    A
    parallel
    B
    skew
    C
    coincident
    D
    none of these

  • If vec (a)= 2 hat (i) - hat (j) + hat (k) and vec(b) = - hat (i) + 3 hat (j) + 4 hat (k) , then value of vec (a). vec(b) is -

    A
    1
    B
    3
    C
    `-3`
    D
    `-1`

    • Similar Questions

    Explore conceptually related problems

    Points A and B have position vector vec(a)=-3hat(i)+2hat(j)+7hat(k) and vec(b)=3hat(i)+4hat(j)-5hat(k) respectively. Find : The direction ratios of vec(AB)

    If vectors vec (a) = p hat (i) + 8 hat (j) + 6 hat (k) and vec (b) = - 3 hat (i) + 4 hat (j) + q hat (k) are parallel , find p and q

    If vec(a)=2hat(i)-5hat(j)+3hat(k) " and " vec(b)=hat(i)-2hat(j)-4hat(k) , find the value of abs(3vec(a)+2vec(b)).

    (i) If the position vectors of the points A, B, C be 5hat(i)+3hat(j)+4hat(k), hat(i)+5hat(j)+hat(k) " and " -3hat(i)+7hat(j)-2hat(k) respectively, then show that the points B bisects the line-segment bar(AC) . (ii) The position vectors of the points P and Q are 5hat(i)-12hat(j)+5hat(k) " and " -4hat(i)+3hat(j)-hat(k) respectively. Find the position vectors of the trisection points of the line-segment bar(PQ) .

    If vec(a)=2hat(i)+3hat(j)-4hat(k) " and " vec(b)=hat(i)+2hat(j)+hat(k) , then find (vec(a)+vec(b)) " and " abs(vec(a)+vec(b)).

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