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

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 angle between the vectors (hat i + hat j + hat k) and ( hat i - hat j -hat k) is

Find the vector equation of the plane passing through the points having position vectors hat i+hat j-2hat k,2i-hat j+hat k and hat i+2hat j+hat k

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 ia n d hatjdot Then its new position is a.+-( hat i)/(sqrt(2))+-( hat j)/(sqrt(2)) b. +-( hat i)/2+-( hat j)/2-( hat k)/(sqrt(2)) c. ( hat i)/(sqrt(2))-( hat k)/(sqrt(2)) d. none of these

Find the vector equation of a plane passing through a point having position vector 2 hat i- hat j+ hat k and perpendicular to the vector 4 hat i+2 hat j-3 hat kdot

The position vectors of the points P and Q are 5 hat i+7 hat j- 2 hat k and -3 hat i+3 hat j+6 hat k respecively. The vector vec A=3 hat i-hat j+hat k passes through the point P and the vector vec B=-3 hat i+2 hat j+4 hat k passes through the point Q. A third vector 2 hat i+7 hat j- 5hat k intersects vectors vec A and vec B . Find the position vectors of the points of intersection

The position vector of the points Pa n dQ are 5 hat i+7 hat j-2 hat k and -3 hat i+3 hat j+6 hat k , respectively. Vector vec A=3 hat i- hat j+ hat k passes through point P and vector vec B=-3 hat i+2 hat j+4 hat k passes through point Q . A third vector 2 hat i+7 hat j-5 hat k intersects vectors Aa n dBdot Find the position vectors of points of intersection.

Find the equation of the line in vector and in cartesian form that passes through the point with position vector 2hat i-hat j+4hat k and is in the direction hat i+2hat j-hat k

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 vector equation of plane passing through the points 2hat i+hat j-hat k and -hat i+3hat j+4hat k and perpendicular to the plane vec r*(hat i-2hat j+4hat k)=10