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VECTORS 1. Define coplanar vectors. Definition : Three or more vectors lie on the same plane are called as coplanar vectors. 2. Define collinear vectors. Definition : Two or more vectors are said to be collinear vectors, when they are along the same lines or parallel lines. If a and b are parallel vectors then a = kb. For any scalar ‘k’. 3. If a = 2 i + 3j – 5k, ( i ) Find the unit vector in the direction of the vector a ( ii ) Find the direction cosines of the vector a and hence prove that, Cos 2 α + Cos 2 β + Cos 2 γ= 1 Solution : consider, a = 2 i + 3j – 5k = ( 2 , 3 , - 5 ) | a | = √ ( 4 + 9 + 25 ) = √ 38 units a 2 i + 3j – 5k ( i ) the unit vector in the direction of the vector a = = | a | √ 38 ( ii ) direction cosines of a are cos α = 2/√ 38 , Cosβ = 3/√ 38 & Cosγ = - 5 / √ 38 Consider, Cos 2 α + Cos 2 β + Cos 2 γ = 4/38 + 9/38 + 25/38 = 1
