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.

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(PA).vec(PB) >0 , then point P lies exterior to the sphere with A B as its diameter.

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

let vec a = 2hat i +3hat j and vec b = hat i +4hat j then find projection of vec a on vec b

If vec a= i- j and vec b=- j+2k ,find (vec a-2 vec b)dot( vec a+ vec b)

If vec a=2 vec i+3 vec j- vec k , vec b=- vec i+2 vec j-4 vec k a n d vec c= vec i+ vec j+ vec k , then find thevalue of ( vec axx vec b) dot ( vec axx vec c)dot

Find a unit vector vec c if vec -i+vec j-vec k bisects the angle between vec c and 3 vec i+4vec j .

Statement 1:Let A( vec a),B( vec b)a n dC( vec c) be three points such that vec a=2 hat i+ hat k , vec b=3 hat i- hat j+3 hat ka n d vec c=- hat i+7 hat j-5 hat kdot Then O A B C is a tetrahedron. Statement 2: Let A( vec a),B( vec b)a n dC( vec c) be three points such that vectors vec a , vec ba n d vec c are non-coplanar. Then O A B C is a tetrahedron where O is the origin.

Find the projection of vec a on vec b , if vec a . vec b =8 and vec b=2 hat i + 6 hat j + 3 hat k .

If vec a=3 hat i- hat j+2 hat k\ a n d\ vec b=2 hat i+ hat j- hat k\ t h e n find ( vec axx vec b) vec adot

A force vec F = (5 vec i+ 3 vec j+ 2 vec k) N is applied over a particle which displaces it from its origin to the point vec r=(2 vec i- vec j) m . The work done on the particle in joules is.