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`

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

If vec(A) = 3 hat(i) + 4 hat(j) and vec(B) = 7 hat(i) + 24 hat(j) , then find a vector having the same magnitudes as vec(B) and parallel to vec(A) .

If vec r is a vector of magnitude 21 and has direction ratios 2,-3a n d6, then find vec rdot

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

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

If vec a, vec b, vec c are any three mutually perpendicular vectors of equal magnitude a, then |vec a+ vec b+ vec c| is equal to

If three unit vectors vec a , vec b ,a n d vec c satisfy vec a+ vec b+ vec c=0, then find the angle between vec aa n d vec bdot

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