Question

If the straight line 3x-5y=7 and 4x+ay=0 are perpendicular to each other, then find the value of a​

Answer 1

Answer:

12/5

Step-by-step explanation:

Any two straight lines that are perpendicular to each other having slopes m1 and m2 are related such that :-

m1 m2 = -1

Also the slope of any line : ax + by +c=0 is given by -a/b.

So the above lines have slopes 3/5 and -4/a respectively

Now since they are perpendicular, 3/5 * -4/a = -1

Now find a.

Answer 2

Answer:

a = 12/5

Step-by-step explanation:

L1 : 3x - 5y = 7 or y = 3x/5 - 7/5

Hence slope m1 = 3/5

L2 : 4x +ay = 0 or y = -4x/a

Hence slope m2 = -4/a

Since the line are perpendicular than,

m1 * m2 = -1

(3/5) * (-4/a) = -1

a = 12/5