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If vec(A) is 2hat(i)+9hat(j)+4hat(k), th...

If `vec(A)` is `2hat(i)+9hat(j)+4hat(k)`, then `4vec(A)` will be `:`

A

`8hat(i)+16hat(j)+36hat(k)`

B

`8hat(i)+36hat(k)+16hat(j)`

C

`8hat(i)+9hat(j)+16hat(k)`

D

`8hat(i)+36hat(j)+16hat(k)`

Text Solution

Verified by Experts

The correct Answer is:
D
`vec(A)=2hat(i)+9hat(j)+4hat(k)`
`4vec(A)=8hat(i)+36hat(j)+16hat(k)`
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verify that vec(a) xx (vec(b)+ vec(c))=(vec(a) xx vec(b))+(vec(a) xx vec(c)) , "when" (i) vec(a)= hat(i)- hat(j)-3 hat(k), vec(b)= 4 hat(i)-3 hat(j) + hat(k) and vec(c)= 2 hat(i) - hat(j) + 2 hat(k) (ii) vec(a)= 4 hat(i)-hat(j)+hat(k), vec(b)= hat(i)+hat(j)+ hat(k) and vec(c)= hat(i)- hat(j)+hat(k).

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Knowledge Check

  • If angle bisector of vec(a) = 2hat(i) + 3hat(j) + 4hat(k) and vec(b) = 4hat(i) - 2hat(j) + 3 hat(k) is vec(c) = alpha hat(i) + 2hat(j) + beta hat(k) then :

    A
    `vec(c). hat(k) + 7= 0`
    B
    `vec(c) .hat(k) - 14 = 0`
    C
    `vec(c) .hat(k) + 14 = 0 `
    D
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  • If vec(A) = 3hat(i) - 4hat(j) + hat(k) and vec(B) = 4hat(j) + phat(i) + hat(k) for what value of p, vec(A) and vec(B) will ve collinear ?

    A
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    B
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    C
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    D
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  • Let vec(A)=2hat(i)-3hat(j)+4hat(k) and vec(B)=4hat(i)+hat(j)+2hat(k) then |vec(A)xx vec(B)| is equal to

    A
    440
    B
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    C
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    D
    `4sqrt(65)`

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