A vector `4hat i+3hat j` rotates about its tail through an angle `53^(@)` in anticlockwise direction then the new vector is

A vector hati+sqrt(3)hatj rotates about its tail through an angle 60^(@) in clockwise direction then the new vector is

Vector vec OA=hat i+2hat j+2hat k turns through a right angle passing through the positive x-axis on the way.Show that the vector in its new position is (4hat i-hat j-hat k)/(sqrt(2))

The vector hat(i)+xhat(j)+3hat(k) is rotated through an angle theta and doubled in magnitude then it becomes 4hat(i)+(4x-2)hat(j)+2hat(k) . The value of x is

Find the resultant of vectors vec a=hat i-hat j+2hat k and vec b=hat i+2hat j-4hat k. Find the unit vector in the direction of the resultant vector.

If bar a=hat i+hat j-4hat k and bar(b)=hat 4i-hat j-2hat k then find (i) a unit vector in the direction of the vector (2bar(a)-bar(b))

A line passes through the point with position vector 2hat i-3hat j+4k is in the direction of 3hat i+4hat j-5hat k. Find the equations of the line in vector and Cartesian forms.

The unit vector perpendicular to both the vectors a=hat i+hat j+hat k and b=2hat i-hat j+3hat k and making an acute angle with the vector k is

If the vectors 3hat i+hat j-2hat k,hat i-3hat j+4hat k are diagonals of a quadrilateral then the area vector of the quadrilateral is

The vector vec OA=-2hat i+hat j+2hat k tum by a right angle about origin (O) so that it passes through hat j+hat k, then vector in new position is

The distance of point B with position vector hat i+2hat j+3hat k from the line passing through the point with position vector 4hat i+2hat j+2hat k and parallel to the vector 2hat i+3hat j+6hat k is :