Question

The position vectors of points P and Q are p⃗ and q⃗ respectively. The point R divides line segment PQ in the ratio 3 : 1 and S is the mid-point of line segment PR. The position vector of S is :

Assertion (A) : The vectors a⃗ = 6î + 2ĵ − 8k̂, b⃗ = 10î − 2ĵ − 6k̂ and c⃗ = 4î − 4ĵ + 2k̂ represent the sides of a right angled triangle. Reason (R) : Three non-zero vectors of which none of two are collinear forms a triangle if their resultant is zero vector or sum of any two vectors is equal to the third.

Position vector of the mid-point of line segment AB is 3î + 2ĵ - 3k̂. If position vector of the point A is 2î + 3ĵ - 4k̂, then position vector of the point B is

In △ABC, AB→ = î + ĵ + 2k̂ and AC→ = 3î − ĵ + 4k̂. If D is mid-point of BC, then vector AD→ is equal to :