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`

A(3,-1,2),B(2,-3,3) and C(1,-2,1) are three given points . Find the angle between the vectors vec(BA)and vec(BC) .

If the angel between unit vectors vec aa n d vec b60^0 , then find the value of | vec a- vec b|dot

Find the equation of the plane passing through A(2,2,-1),B(3,4, 2)a n dC(7,0,6)dot

If vec a , a n d vec b are unit vectors , then find the greatest value of | vec a+ vec b|+| vec a- vec b|dot

If | vec a|=| vec b|=| vec a+ vec b|=1, then find the value of | vec a- vec b|dot

Find the magnitude of the vector vec(A)=hati-2hatj+3hatk .Also find the unit vector in the direction of vec(A) .

If ( vec axx vec b)^2+( vec a.vec b)^2=144 and | vec a|=4, then find the value of | vec b|dot

If vec ba n d vec c are two-noncollinear vectors such that vec a||( vec bxx vec c), then prove that ( vec axx vec b) . ( vec axx vec c) is equal to | vec a|^2( vec bdot vec c)dot

If vec aa n d vec b are two vectors of magnitude 1 inclined at 120^0 , then find the angle between vec ba n d vec b- vec adot

A ,B ,C and D have position vectors vec a , vec b , vec c and vec d , respectively, such that vec a- vec b=2( vec d- vec c)dot Then a. A Ba n dC D bisect each other b. B Da n dA C bisect each other c. A Ba n dC D trisect each other d. B Da n dA C trisect each other