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Find the unit vector in the direction of sum of vectors `veca=hat2i-hatj+hatk` and `vecb=2hatj+hatk.`

Text Solution

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The correct Answer is:
Let `vecc` denote the sum of `vecaandvecb`.
We have, `veccandveca+vecb`
`=2hati-hatj+2hatj+hatk=2hati+hatj+2hatk`
:.Unit vector in the direction of `vecc=(vecc)/(|veca|)=(2hati+hatj+2hatk)/(sqrt2^(2)+1^(2)+2^(2))=(2hati+hatj+2hatk)/(sqrt9)`
`hatc=(2hati+hatj+2hatk)/(3)`
Let `vecc` denote the sum of `vecaandvecb`.
We have, `veccandveca+vecb`
`=2hati-hatj+2hatj+hatk=2hati+hatj+2hatk`
:.Unit vector in the direction of `vecc=(vecc)/(|veca|)=(2hati+hatj+2hatk)/(sqrt2^(2)+1^(2)+2^(2))=(2hati+hatj+2hatk)/(sqrt9)`
`hatc=(2hati+hatj+2hatk)/(3)`
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Knowledge Check

  • A unit vector in the direction of resultant vector of vecA = -2hati + 3hatj + hatk and vecB = hati + 2 hatj - 4 hatk is

    A
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    B
    `(hati+2hatj-4hatk)/(sqrt(35))`
    C
    `(-hati+5hatj-3hatk)/(sqrt(35))`
    D
    `(-3hati+hatj+5hatk)/(sqrt(35))`

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