Position vector ` hat k` is rotated about the origin by angle `135^0` in such a way that the plane made by it bisects the angle between ` hat i` and `hatj`. Then its new position is

Find out the angle between two-vectors hat i + hat j and hat i- hat k .

Find the cosine of the angle made by the vector (2hat i-3hatj+6hatk) with the posititve z-axis.

Find the angle made by the vector sqrt(2) hat (i) + hat (j) + hat (k) with the y - axis

Find the scalar product of the following pair of vectors and the angle between them : hat (i) + hat(j) and hat (j) + hat (k)

Let A ,B ,C be points with position vectors 2 hat i- hat j+ hat k , hat i+2 hat j+3 hat ka n d3 hat i+ hat j+2 hat k respectively. Find the shortest distance between point B and plane O A Cdot

Find the angle of vector vec a = 6 hat i + 2 hat j - 3 hat k with x -axis.

The position vectors of the points Pa n dQ with respect to the origin O are vec a= hat i+3 hat j-2 hat k and vec b=3 hat i- hat j-2 hat k , respectively. If M is a point on P Q , such that O M is the bisector of angleP O Q , then vec O M is a. 2( hat i- hat j+ hat k) b. 2 hat i+ hat j-2 hat k c. 2(- hat i+ hat j- hat k) d. 2( hat i+ hat j+ hat k)

Find the angle between the vectors hat i-2 hat j+3 hat k and 3 hat i-2 hat j+ hat kdot

If vec a=7 hat i-4 hat j-4 hat k and vec b=-2 hat i- hat j+2 hat k , determine vector vec c along the internal bisector of the angle between of the angle between vectors vec a and vec b such that | vec c| =5sqrt(6)

Angle in (rad) made by the vector ( sqrt3 hat i +hat j ) with X-axis is: