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Let -> aand -> bbe two unit vectors a...

Let ` -> a`and ` -> b`be two unit vectors and is the angle between them. Then ` -> a+ -> b`is a unit vector if(A) `theta=pi/4` (B) `theta=pi/3` (C) `theta=pi/2` (D) `theta=(2pi)/3`

Text Solution

Verified by Experts

We are given, `veca,vecb and veca+vecb` all are unit vector which means
`|veca| = |vecb| = |veca+vecb| = 1`
Now, `|veca+vecb| = 1`
`=>(|veca+vecb|)^2 = 1`
`=>(|veca+vecb|)^2 = 1`
`=>(veca+vecb).(veca+vecb) = 1`
`=>veca.veca +veca.vecb + vecb.veca+vecb.vecb= 1`
`=>|a|^2+2veca.vecb+|b|^2=1`
...
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Knowledge Check

  • Let vec(a) and vec(b) be two unit vectors and theta is the angle between them. Then vec(a)+vec(b) is a unit vector if :

    A
    `theta = (pi)/(4)`
    B
    `theta =(pi)/(3)`
    C
    `theta=(pi)/(2)`
    D
    `theta=(2pi)/(3)`

  • If a and b are unit vectors and theta is the angle between them, then a+b is a unit vector if theta equals

    A
    `(2pi)/3`
    B
    `pi/3`
    C
    `pi/2`
    D
    `pi/4`

  • Let a and b are unit vectors and theta is the angle between them, then a-sqrt3 b will also be a unit vector if value of theta is

    A
    `pi/3`
    B
    `pi/4`
    C
    `pi/6`
    D
    `(2pi)/3`

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