The vertices A , B and C of ∆ A B C are 1 , - 2 , - 7,6 and 11 5 , 2 5 respectively. The measure of the interior angle A of the ∆ A B C lies in

Question

The vertices A , B and C of ∆ A B C are 1 , - 2 , - 7,6 and 11 5 , 2 5 respectively. The measure of the interior angle A of the ∆ A B C lies in, 75 o , 90 o, 60 o , 75 o, 45 o , 60 o, 120 o , 150 o

MARKS App · Accepted Answer

We have A B → = - 8 i ^ + 8 j ^ = 8 - i ^ + j ^ , A C → = 11 5 - 1 i ^ + 2 5 + 2 j ^ = 6 5 i ^ + 12 5 j ^ = 6 5 i ^ + 2 j ^ ∴ cos ⁡ θ = - i ^ + j ^ ⋅ i ^ + 2 j ^ 2 5 = - 1 + 2 10 = 1 10 ⇒ tan ⁡ θ = 3 ⇒ tan ⁡ θ ∈ 3 , 2 + 3 Hence, θ ∈ 60 ° , 75 °

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