Q16 of 177 Page 24

If are the position vectors of the vertices of an equilateral triangle whose orthocentre is at the origin, then write the value of .

Since in an equilateral triangle, orthocenter and centroid coincide, therefore the position vector of centroid is .

Also, the position vector of centroid G () can be defined as

Therefore, hence

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.

Write a unit vector making equal acute angles with a coordinates axes.

If a vector makes angles α, β, γ with OX, OY and OZ respectively, then write the value of sin²α + sin²β + sin²γ.