The ratio in which `hat i+2hat j+3hat k` divides the join of `-2hat i+3hat j+5hat k` and `7hat i-hat k` is

Find the vector of length 3 unit which is perpendicular to hat i+hat j+hat k and lies in the plane of hat i+hat j+hat k and 2hat k-3hat j

the angle between the vectors 2hat i-3hat j+2hat k and hat i+5hat j+5hat k is

Vectors perpendicular to hat i-hat j-hat k and in the plane of hat i+hat j+hat k and -hat i+hat j+vec k are hat i+hat k b.2hat i+hat j+hat hat k c.3hat i+2hat j+hat k d.-4hat i-2hat j-2hat k

Find the area of the parallelogram determined by the vectors: 2hat i and 3hat j2hat i+hat j+3hat k and hat i-hat j3hat i+hat j-2hat k and hat i-3hat j+4hat khat i-3hat j+hat k and hat i+hat j+hat k

underset with a = 2hat i + hat j-3hat k, vec b = -hat i + hat j + 2hat k, vec c = 4hat i + 3hat k

A point on the line hat r=2hat i+3hat j+4hat k+t(hat i+hat j+hat k) is

Show that the points A(-2 hat i+3 hat j+5 hat k), B( hat i+2 hat j+3 hat k) and C(7 hat i-3 hat k) are collinear.

Find the projection of vector hat i+3hat j+7hat k on the vector 7hat i-hat j+8hat k

Show that the points whose position vectors are as given below are collinear: 2hat i+hat j-hat k,3hat i-2hat j+hat k and hat i+4hat j-3hat k3hat i-2hat j+4hat k,hat i+hat j+hat k and -hat i+4hat j-2hat k

If t is a real number, and a vector vec r satisfies the equation vec r times(hat i-2hat j+hat k)=hat i-hat k , then vec r can be equal to- (A) hat j+t(hat i-2hat j+hat k) (B) hat i-hat j+hat k (C) 2hat i-3hat j+2hat k (D) hat i+hat k