If the adjacent sides of a rectangle are a ˉ = 5 m ˉ − 3 n ˉ , b ˉ = − m ˉ − 2 n ˉ and the adjacent sides of another rectangle are c ˉ = − 4 m ˉ − n ˉ , d ˉ = − m ˉ + n ˉ , then the angle between the vectors x ˉ = 3 a ˉ + c ˉ + d ˉ and y ˉ = 5 c ˉ + d ˉ is

Question

If the adjacent sides of a rectangle are a ˉ = 5 m ˉ − 3 n ˉ , b ˉ = − m ˉ − 2 n ˉ and the adjacent sides of another rectangle are c ˉ = − 4 m ˉ − n ˉ , d ˉ = − m ˉ + n ˉ , then the angle between the vectors x ˉ = 3 a ˉ + c ˉ + d ˉ ​ and y ˉ ​ = 5 c ˉ + d ˉ ​ is, 2 π ​, Cos − 1 ( 5 43 ​ 19 ​ ), Cos − 1 ( 5 43 ​ 19 ​ ) + π, Sin − 1 4 43 ​ 19 ​

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