Find a unit vector perpendicular to eac...

Find a unit vector perpendicular to each of the vectors `vec a + vec b and vec a - vec b,` where `veca=3hati+2hatj+2hatk and vecb=hati+2hatj-2hatk.`

Text Solution

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The correct Answer is:

`(1)/(3)(2hat(i)-2hat(j)-hat(k))`.

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Find a vector and unit vector perpendicular to each of the vector veca+vecb and veca-vecb Where veca = 3hati+2hatj+2hatk & vecb = hati+2hatj-2hatk .

Find a unity vector perpendicular to each of the vectors (veca+vecb) and (veca-vecb) , where veca=hati+hatj+hatk and vecb=hati+2hatj+3hatk

Knowledge Check

A unit vector perpendicular to each of the vectors a+b and a-b, where a= 3hati + 2hatj + 2hatk and b= hati + 2hatj -2hatk is

A

`1/3 hati - 1/3 hat j - 1/3 hatk` or `-1/3 hat i+ 1/3 hatj + 1/3 hatk`

B

`4/3 hati - 4/3 hat j - 4/3 hatk` or `-4/3 hat i + 4/3 hatj + 4/3 hatk`

C

`2/3 hati - 2/3 hat j - 1/3 hatj` or `-2/3 hat i + 2/3 hatj + 1/3 hatk`

D

None of the above

Find a unit vector perpendicular to each one of the vectors vec a =4hati -hatj +3hatk and vecb =3 hati +2hatj -hatk

A

`(-5 hati+13 hatj+11hatk)/(sqrt315)`

B

`(5hati-3hatj +12 hatk)/(sqrt215)`

C

`(-hati+5hatj+11hatk)/(sqrt305)`

D

`(hati+3hatj+5hatk)/(sqrt400)`

The vector vec(A)=6hati+9hatj-3hatkand vecB=2hati+3hatj-hatk are

A

parallel

B

antiparallel

C

perpendicular

D

identical

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Find vecaxxvecb and |vecaxxvecb| if vec=2hati+hatj+3hatk and vecb=3hati+5hatj-2hatk

Find the unit vector perpendicular to each of the vectors veca = 3hati+2hatj-3hatk and vecb = hati+hatj-hatk .

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Find a unit vector perpendicular the vectors vec(A) = 4 hati = hatj +3 hatk and vec(B) =- 2hati + hatj - 2hatk .

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