Given three points are `A(-3,-2,0),B(3,-3,1)a n dC(5,0,2)dot` Then find a vector having the same direction as that of ` vec A B` and magnitude equal to `| vec A C|dot`

Given three points are A(-3,-2,0),B(3,-3,1) and C(5,0,2) Then find a vector having the same direction as that of vec AB and magnitude equal to |vec AC|

Find a unit vector in the direction of vec(AB) , where A(1, 2, 3) and B( 2, 3, 5) are the given points.

If vec A=(1,1,1) , vec C=(0,1,-1) are two given vectors, then find a vector vec B satisfying the equations vec A xx vec B=vec C and vec A * vec B=3 .

A vector vec A when added to the vector vec B = 3. 0 hat i+ 4 hat j yields a resultant vector that is in the positive y-direction and has a magnintude equal to that of vec B . Find the magnitude of vec A .

If vec a = (2,-2,1) , vec b = (2,3,6) and vec c = (-1,0,2) ,Find the magnitude and direction of vec a + vec b - 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

For any tow vectors a\ a n d\ b show that ( vec a+ vec b) ( vec a- vec b)=0 if | vec a|=| vec b|dot