`P` is a point on the line through the point `A` whose position vector is ` vec a` and the line is parallel to the vector ` vec b` . If `P A=6,` the position vector of `P` is: (a)` vec a+6 vec b` (b) ` vec a+6/(| vec b|) vec b` (c)` vec a-6 vec b/(| vec b|)` (d) ` vec b+6/(| vec a|) vec a`

If the position vector of a point A is vec a + 2 vec b and vec a divides AB in the ratio 2:3 , then the position vector of B, is

If the position vectors of the points A(3,4),B(5,-6) and (4,-1) are vec a , vec b , vec c respectively compute vec a+2 vec b-3 vec c

The position vectors of A, B,C and D are vec a , vec b , vec 2a+ vec 3b and vec a - vec 2b respectively show that vec DB=3 vec b -vec a and vec AC =vec a + vec 3b

If the position vectors of the points A(3,4),B(5,-6) and C (4,-1) are vec a , vec b , vec c respectively compute vec a+2 vec b-3 vec c

For any two vectors vec a and vec b , show that : ( vec a+ vec b)dot( vec a- vec b)=0, when | vec a|=| vec b|dot

If vec a , vec b are two vectors, then write the truth value of the following statements: vec a=- vec b| vec a|=| vec b| | vec a|=| vec b| vec a=+- vec b | vec a|=| vec b| vec a= vec b

For any vector vec a\ a n d\ vec b prove that | vec a+ vec b|lt=| vec a|+| vec b|dot

Prove that four points 2 vec a+3 vec b- vec c , vec a-2 vec b+3 vec c ,3 vec a+4 vec b-2 vec c and vec a-6 vec b+6 vec c are coplanar.

The length of the perpendicular form the origin to the plane passing through the point a and containing the line vec r= vec b+lambda vec c is a. ([ vec a vec b vec c])/(| vec axx vec b+ vec bxx vec c+ vec cxx vec a|) b. ([ vec a vec b vec c])/(| vec axx vec b+ vec bxx vec c|) c. ([ vec a vec b vec c])/(| vec bxx vec c+ vec cxx vec a|) d. ([ vec a vec b vec c])/(| vec cxx vec a+ vec axx vec b|)

If vec b is a unit vector such that ( vec a+ vec b)dot ( (vec a- vec b))=8,\ find \ | vec a|dot