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

If `vec(a)= 2vec(i)-3 vec(j) + vec(k). vec(b)= vec(i) + 4vec(j)- 2vec(k)`, then find `(vec(a) + vec(b)) xx (vec(a) - vec(b))`.

Text Solution

Verified by Experts

The correct Answer is:
`-2(2vec(i) + 5vec(j) + 11vec(k))`
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vec(a)= 2vec(i) + vec(j) -vec(k), vec(b)= -vec(i) + 2vec(j)- 4vec(k) and vec(c )= vec(i) + vec(j) + vec(k) , then find (vec(a) xx vec(b)).(vec(b) xx vec(c )) .

If vec(a)= vec(i) + vec(j)+ vec(k), vec(c )= vec(j)- vec(k) , then find vector vec(b) such that vec(a) xx vec(b)= vec(c ) and vec(a).vec(b)= 3

Knowledge Check

  • If vec(a)= 3 vec(i)- vec(j)-2vec(k), vec(b)= 2vec(i) + 3vec(j) + vec(k) , then (vec(a) + 2vec(b)) xx (2vec(a) - vec(b)) =

    A
    `-25 vec(i) + 35 vec(j) -55vec(k)`
    B
    `25 vec(i)-35 vec(j) + 55vec(k)`
    C
    `25 vec(i) + 35vec(j)- 55vec(k)`
    D
    `-25vec(i) -35vec(j)-55vec(k)`

  • If vec(a)= 2vec(i)-vec(j) +vec(k), vec(b)= 3vec(i) + 4vec(j) -vec(k) , then |vec(a) xx vec(b)|=

    A
    `sqrt135`
    B
    `sqrt145`
    C
    `sqrt155`
    D
    `sqrt165`

  • If vec(a)= vec(i) + vec(j) + vec(k), vec(b)= 2vec(i)-3vec(j) + vec(k) , then (vec(a) xx vec(b))/(|vec(a) xx vec(b)|) + (vec(b) xx vec(a))/(|vec(b) xx vec(a)|) =

    A
    `vec(0)`
    B
    `2vec(i) + vec(j)-2vec(k)`
    C
    `vec(i)+vec(j) + 2vec(k)`
    D
    `vec(i) + 2vec(j) -vec(k)`

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