Distance between two points whose position vectors are `3 hat i+hat j-2 hat k` and `hat i-3 hat j+5 hat k` is (a) 69 units (b) `sqrt69` units (c) 13 units (d) 29 units

The unit vector in the direction of the sum of vectors hat i + hat j + hat k and 2 hat i + 3 hat j + 4 hat k is

The unit vector perpendicular to vec A = 2 hat i + 3 hat j + hat k and vec B = hat i - hat j + hat k is

A unit vector perpendicular to the vectors veca = 2 hat i - 6 hat j - 3 hat k and vec b = 4 hat i + 3 hat j - hat k is

A unit vector perpendicular to the plane passing through the points whose position vectors are hat i-hat j+2hat k,2hat i-hat k and 2hat i+hat k is

A line passes through two points whose position vectors A(hat i+hat j-2hat k) and B(hat i-3hat j+hat k) .Then the position vector of a point on it at a unit distance from A and closet to B

A line passes through two points whose position vectors A(hat i+hat j-2hat k) and B(hat i-3hat j+hat k) .Then the position vector of a point on it at a unit distance from A and closet to B

Show that the area of a parallelogram having diagonals 3 hat i+ hat j-2 hat k\ a n d\ hat i-3 hat j+4 hat k is 5sqrt(3) square units.

A line passes through the points whose pdotvdot are hat i+ hat j-2 hat k and hat i-3 hat j+ hat k .The position vector of a point on it at unit distance from the first point is

Find a unit vector parallel to the resultant of vectors vec A = 3 hat I + 3 hat j - 2 hat k and vec B= hat i- 5 hat j + hat k .

Show that the points whose position vectors are 5hat(i) + 5 hat(k), 2 hat(i) + hat(j) + 3 hat(k) and -4 hat(i) + 3 hat(j) - hat(k) are collinear.