If `vecr=xhati+yhatj+zhatk`, find : `(hatrxxhati)*(hatrxxhatj)+xy`.

If vecr=xhati+yhatj+zhatk , find : (vecrxxhati)*(vecrxxhatj)+xy .

If veca=xhati + y hatj + zhatk, vecb= yhati + zhatj + xhatk and vecc= zhati + xhatj+ yhatk , " then " vecaxx (vecbxx vecc) is (a)parallel to ( y- z) hati + (z - x) hatj + (x -y) hatk (b)orthogonal to hati + hatj + hatk (c)orthogonal to ( y+z) hati + ( z + x) hatj + ( x + y) hatk (d)orthogonal to xhati + yhatj + zhatk

If veca= x hati+yhatj+zhatk, vecb= yhati+zhatj+xhatk, vecc=zhati+xhatj+yhatk , then vecaxx(vecbxxvecc) is :

Find the vector equation of the line passing through (1, 2, 3) and parallel to each of the planes vecr = (hati-hatj+2 hatk)= 5" and "vecr *(3hati- hatj+hatk)= 6 . Also find the point of intersection of the line thus obtained with the plane vecr * (2hati-hatj+hatk)= 4 .

If veca=xhati+2hatj-zhatk and vecb=3hati-yhatj+hatk are equal vectors. Write the value of x+y+z .

Find the acute angle between the planes vecr.(hati+2hatj-hatk)=3 and vecr.(2hati-hatj+2hatk)=2 .

Find the values of x,y and z so that the vectors : veca=xhati+2hatj+zhatk and vecy=2hati+yhatj+hatk are equal.

If the vectors xhati+hatj+hatk,hati+yhatj+hatk and hati+hatj+zhatk are coplanar where, x ne1,y ne1 and z ne1 , then prove that (1)/(1-x)+(1)/(1-y)+(1)/(1-z)=1

Find whether the lines: vecr=(hati-hatj-hatk)+lambda(2hati+hatj) and vecr=(2hati-hatj)+mu (hati+hatj-hatk) intersect or not. If itersecting, find their point of intersection..

In the electric field vecE = 3x hati - 2y hatj + 5zhatk , find the potential difference between the ponts A(1,3,5) and B(3,2,7)