Q13 of 177 Page 24

If D is the mid-point of side BC of a triangle ABC such that write the value of λ.

Let the position vectors of A, B and C be and

Then the position vector of will be

Any vector , if the position vectors of point A () and B () are known, can be written as .

Then,

⇒

Substituting value of , we get

⇒ or λ=2

If G denotes the centroid of Δ ABC, then write the value of

If denote the position vectors of points A and B respectively and C is a point on AB such that 3AC = 2AB, then write the position vector of C.

If D, E, F are the mid-points of the sides BC, CA and AB respectively of a triangle ABC, write the value of

If is non-zero vector of modulus a and m is a non-zero scalar such that m is a unit vector, write the value of m.