PROBLEMS ON COPLANAR VECTORS

Problem 1 :

Determine whether the three vectors

are coplanar.

Solution :

Problem 2 :

Let 

If c₁ = 1 and c₂ = 2, find c₃ such that 

are coplanar.

Solution :

After applying the values of c₁ and c₂, we get

Problem 3 :

If 

show that 

depends on neither x nor y.

Solution :

Problem 4 :

If the vectors 

are coplanar, prove that c is the geometric mean of a and b

Solution :

Since the vectors are coplanar,

Problem 5 :

Let

the three non zero vectors such that c vector is a unit perpendicular to both a vector and c vector. If the angle between a vector and b vector is π/6, show that

Solution :

c vector is perpendicular to both a vector and b vector. So, c vector is parallel to (a vector x b vector)

Squaring on both sides,