Home
Class 12
MATHS
Let vec a=2i+j+k , vec b=i+2j-k and a u...

Let ` vec a=2i+j+k , vec b=i+2j-k` and a unit vector ` vec c` be coplanar. If ` vec c` is perpendicular to ` vec a ,` then ` vec c` is `1/(sqrt(2))(-j+k)` b. `1/(sqrt(3))(-i-j-k)""` c. `1/(sqrt(5))(-k-2j)` d. `1/(sqrt(3))(i-j-k)`

A

`1/sqrt2(-j+k)`

B

`1/sqrt3(i-j-k)`

C

`1/sqrt5(i-2j)`

D

`1/sqrt3(i-j-k)`

Text Solution

AI Generated Solution

To solve the problem, we need to find the unit vector \(\vec{c}\) that is coplanar with vectors \(\vec{a}\) and \(\vec{b}\), and is also perpendicular to \(\vec{a}\). ### Step 1: Define the vectors Given: \[ \vec{a} = 2\hat{i} + \hat{j} + \hat{k} \] \[ ...
Promotional Banner

Similar Questions

Explore conceptually related problems

Let vec a=2hat i+hat j+hat k,hat b=hat i+2hat j-hat k and a unit vector vec c be coplanar.If vec c is perpendicular to vec a then vec c=+-(1)/(sqrt(2))(-hat j+hat k)( b) (1)/(sqrt(3))(-hat i-hat j-hat k)(1)/(sqrt(5))(hat o-2hat j)(d)(1)/(sqrt(3))(hat i-hat j-hat k)

if vec a=2i+2j+3k,vec b=-i+2j+k and vcec=3i+j are such that vec a+lambdavec b is perpendicular vec c then find the value of lambda

if vec a=2i+j+3k and vec b=3i+5j-2k then |a xx b|

let vec a=hat i+hat j-hat k and vec b=hat i-hat j-hat k and vec c be a unit vector perpendicular to vec a and coplanarwith vec a and vec b then vec c is

If vec a=i+j,vec b=j+k and vec c=k+i write unit vectors parallel to vec a+vec b-2vec -

If vec a = i + j + k & vec b = i-2j + k, then the vector vec c such that vec a * vec c = 2 & vec a xxvec c = vec b is

If vec a=hat i+hat j+hat k and vec b=hat j-hat k, find a vector vec c such that vec a x vec c=vec b and vec a*vec c=3

vec a = i + j + k, vec b = i-j + k, vec c = 2i + 3j-k then (vec aXvec b) Xvec c =

If vec a=i+j+k and vec b=j-k then find vector c, such that a xx c=b and a*c=3

vec a=2hat i-hat j+hat k,vec b=hat i+hat j-2hat k and vec c=hat i+3hat j-hat k,f in d lambda such that vec a is perpendicular to lambdavec b+vec c