`2vec i*3vec j`

Vector of length of 3 unit which is perpendicular to vec i + vec j + vec k and lies in the plane of vec i + vec j + vec k and 2vec i-3vec j, is (1) (3) / (sqrt ( 6)) (vec i-2vec j + vec k) (2) (3) / (sqrt (6)) (2vec i-vec j-vec k) (3) (3) / (sqrt (114)) ( 8vec i-7vec j-vec k) (4) (3) / (sqrt (114)) (- 7vec i + 8vec j-vec k)

Find the unit vector in the direction of the vector vec a + vec b if vec a =vec i +2 vec j + 3 vec k and vec b = 2 vec i + 3 vec j + 5 vec k .

if vec b=2 vec i + 3 vec j - vec k and vec c= vec i + 4 vec j + 5 veck then find a vector vec a such that vec b * vec a =0 and vec c * vec a=0 . Also find the unit vector along vec a .

The position vectors of three A,B, and C in space are respectively 2 vec i + 3 vec j - vec k, vec i - 2 vec j + 3 vec k and 4 vec i + vec j + vec k . Find the volume of the parallelepiped whose three concurrent edges are OA, OB and OC where O is the origin.

If three vector 2vec i-vec j-vec k,vec i+2vec j-3vec k,3vec i+lambdavec j+5vec k are coplanar then the value of lambda is :

Statement 1:vec a=3vec i+pvec j+3vec k and vec b=2vec i+3vec j+qvec k are parallel vectors if p=9/2 and q=2. Statement 2: if vec a=a_(1)vec i+a_(2)vec j+a_(3)vec k and vec b=b_(1)vec i+b_(2)vec j+b_(3)vec k are parallel,then (a_(1))/(b_(1))=(a_(2))/(b_(2))=(a_(3))/(b_(3)) .

Statement 1: let A( vec i+ vec j+ vec k)a n dB( vec i- vec j+ vec k) be two points. Then point P(2 vec i+3 vec j+ vec k) lies exterior to the sphere with A B as its diameter. Statement 2: If Aa n dB are any two points and P is a point in space such that vec P Adot vec P B >0 , then point P lies exterior to the sphere with A B as its diameter.

Let ABCD be the parallelogram whose sides AB and AD are represented by the vectors 2vec i+4vec j-5vec k and vec i+2vec j+3vec k respectively. Then if vec a is a unit vector parallel to vec AC ,then vec a is equal to

The position vectors of the points A and B are vec i + 2 vec j + 3 vec k and 2 vec i - vec j - vec k respectively. Find the projection of vec (AB) on the vector vec i + vec j + vec k . Also find the resolved part of vec (AB) in that direction.

If vec r = 3vec i + 2vec j-5vec kvec a = 2vec i-vec j + vec k, vec b = vec i + 3vec j-2vec k and vec c = -2vec i + vec j-3vec k such that vec r = lambdavec a + muvec b + deltavec c then mu, (lambda) / (2), delta are in? (A) AP (B) GP (C) HP (D) AGP