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

If `vec(a)=hat(i)+2hat(j)+3hat(k),vec(b)=-hat(i)+2hat(j)+hat(k)andvec(c)=3hat(i)+hat(j)" find "lambda" such that "vec(a)+lambdavec(b)` is perpendicular to `vec(c).`

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

If vec a = 2 hat i + 2 hat j + 3 hat k , vec b = - hat i + 2 hat j + hat k and vec c = 3 hat i + hat j are such that vec a + lambda vec b is perpendicular to vec c , then find the value of lambda .

Knowledge Check

  • If vec(a)=hat(i)+2hat(j)+3hat(k),vec(b)=-hat(i)+2hat(j)+hat(k),vec(c)=3hat(i)+hat(j)" then "vec(a)+tvec(b) will be perpendicular to vec(c) only when t =

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    5
    B
    4
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    8
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    `(7)/(3)`

  • If vec(a)=2hat(i)+3hat(j)-hat(k),vec(b)=hat(i)+2hat(j)-5hat(k),vec(c)=3hat(i)+5hat(j)-hat(k), then a vector perpendicular to vec(a) and lies in the plane containing vec(b)andvec(c) is

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    `-17hat(i)+21hat(j)-97hat(k)`
    B
    `17hat(i)+21hat(j)-97hat(k)`
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  • For vec(a)=hat(i)+hat(j)-2hat(k), vec(b)=-hat(i)+2hat(j)+hat(k) and vec(c)=hat(i)-2hat(j)+2hat(k) , then find the unit vector parallal to vec(a)+vec(b)+vec(c) is ...................... .

    A
    `(hat(i)+hat(j)-hat(k))/(sqrt(3))`
    B
    `(hat(i)+hat(j)+hat(k))/(sqrt(3))`
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