Find the 10

Find the value of t if 2tx+5y-6=0 and 5x-4y+8=0 are perpendicular, parallel, what angle does each of the lines make with the x-axis, find the angle between the lines?

Correct result:

t1 =  2
A1 =  -38.6598 °
A2 =  -128.6598 °
t2 =  -3.125
B1 =  51.3402 °
B2 =  -128.6598 °

Solution:

2tx+5y6=0 5x4y+8=0  n1=(2t;5) n2=(5;4)   normal n1.n2=0   2 t1 5+5 (4)=0  10t1=20  t1=22tx+5y-6=0 \ \\ 5x-4y+8=0 \ \\ \ \\ n_{1}=(2t; 5) \ \\ n_{2}=(5; -4) \ \\ \ \\ \ \\ normal \ \\ n_{1}.n_{2}=0 \ \\ \ \\ \ \\ 2 \cdot \ t_{1} \cdot \ 5+5 \cdot \ (-4)=0 \ \\ \ \\ 10t_{1}=20 \ \\ \ \\ t_{1}=2



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