Let P - 2 , - 1 , 1 and Q 56 17 , 43 17 , 111 17 be the vertices of the rhombus P R Q S . If the direction ratios of the diagonal R S are α , - 1 , β , where both α and are integers of minimum absolute values, then α 2 + β 2 is equal to

Step-by-step solution

Given, P - 2 , - 1 , 1 and Q 56 17 , 43 17 , 111 17 be the vertices of the rhombus P R Q S . If the direction ratios of the diagonal R S are α , - 1 , β , where both α and β are integers of minimum absolute values, then α 2 + β 2 is equal to Now R S = α , - 1 , β So, direction ratio of P Q ≡ 56 17 + 2 , 43 17 + 1 , 111 17 - 1 ≡ 90 17 , 60 17 , 94 17 Now we know that diagonal of rhombus are perpendicular, So, 90 17 α + 60 17 - 1 + 94 17 β = 0 ⇒ 90 &