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Let bar a= hat i+ hat j+ hat k ,""b=...

Let ` bar a= hat i+ hat j+ hat k ,""b= hat i- hat j+2 hat k` and ` bar c=x hat i+(x-2) hat j- hat k` . If the vector c lies in the plane of a and b , then x equals (1) 0 (2) 1 (3) `-4` (4) `-2`

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Verified by Experts

`a,b,c` are in simple plane
`[abc]=0`
`[[x,x-2,-1],[1,1,1],[1,-1,2]]=0`
`x(2+1)-(x-2)1+(-1)(-2)=0`
`3x-x+2+2=0`
`2x+4=0`
`x=-2`
option`4=(-2)`
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Knowledge Check

  • Let vec(a) = hat(i) + hat(j) + hat(k),vec(b) = hat(i) - hat(j) + 2hat(k) and vec(c) = xhat(i) + (x-2)hat(j) - hat(k) . If the vector vec(c) lies in the plane of vec(a) and vec(b) then x equals

    A
    0
    B
    1
    C
    `-4`
    D
    `-2`

  • Let vec(a) = hat(i) + hat(j) + hat(k), vec(b) = hat(i) - hat(j) + 2hat(k) and vec(c) = xhat(i) + (x-2)hat(j) - hat(k) . If the vector vec(c) lies in the plane of vec(a) & vec(b) , then x equals

    A
    0
    B
    1
    C
    `-4`
    D
    `-2`

  • Let a=hat(i)+hat(j)+hat(k), b=hat(i)-hat(j)+hat(k) and c=hat(i)-hat(j)-hat(k) be three vectors. A vector v in the plane of a and b whose projection on c is 1/sqrt(3) , is given by

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    B
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    C
    `3hat(i)+hat(j)+3hat(k)`
    D
    `-3hat(i)+hat(j)+3hat(k)`
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