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If vec(a) = 2hat(i) - 3hat(j) + hat(k), ...

If `vec(a) = 2hat(i) - 3hat(j) + hat(k), vec(b) = -hat(i) + hat(k)` and `vec(c) = 2hat(j) - hat(k)` are three vectors, then find the area of the parallelogram having diagonals `(vec(a) + vec(b))` and `(vec(b) + vec(c))`.

Text Solution

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The correct Answer is:
`(1)/(2) sqrt(21)` sq. units
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If vec(a) = xhat(i) + 2hat(j) - z hat(k) and vec(b) = 3hat(i) - y hat(j) + hat(k) are two equal vectors, then find the value of x + y +z.

If vec(a) = 2hat(i) + 3hat(j) + hat(k), vec(b) = hat(i) - 2hat(j) + hat(k) and vec(c) = -3hat(i) + hat(j) + 2hat(k) , then find [vec(a)vec(b)vec(c)] .

Knowledge Check

  • If vec(a)=hat(i)+2hat(j)+hat(k),vec(b)=2hat(i)-2hat(j)+2hat(k) and vec(c)=-hat(i)+2hat(j)+hat(k) , then

    A
    `vec(a)` and `vec(b)` have the same directions
    B
    `vec(a)` and `vec(c)` have opposite directions
    C
    `vec(b)` and `vec(c )` have opposite directions
    D
    no pair of vectors have same directions

  • If vec(A)=hat(i)+2hat(j)-hat(k),vec(b)=hat(i)+hat(j)+2hat(k),vec(c )=2hat(k),vec(c )=2hat (i)-hat(j) , then

    A
    `vec(a)botvec(b )`
    B
    `vec(b)bot vec(c )`
    C
    `vec(a) bot vec(c )`
    D
    no pair of vectors are perpendicular

    • Similar Questions

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    If vec(a) = hat(i) + 2hat(j) + hat(k), vec(b) = 2hat(i) + hat(j) and vec(c) = 3hat(i) - 4hat(j) - 5hat(k) , then find a unit vector perpendicular to both of the vectors (vec(a) - vec(b)) and (vec(c) - vec(b)) .

    Find the altitude of a parallelopiped determined by the vectors vec(a) = hat(i) + hat(j) + hat(k), vec(b) = 2hat(i) + 4hat(j) - hat(k) and vec(c) = hat(i) + hat(j) + 3hat(k) , if the base is taken to the parallelogram determined by vec(a) and vec(b) .

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

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    Find vec(a).vec(b) if vec(a) = -hat(i) + hat(j) - 2hat(k) and vec(b) = 2hat(i) + 3hat(j) - hat(k) .

    If vec(a)=hat(i)+2hat(j)-2hat(k),vec(b)=2hat(i)-hat(j)+hat(k) and vec(c)=hat(i)+3hat(j)-hat(k) , then find the value of vec(a)xx(vec(b)xxvec(c)) .

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