If the lines 3x+y=4, x-ay+7=0 and bx+2y+5=0 form three consecutive sides of a rectangle, find the values of a and b.
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L1: 3 x + y = 4
L2: x - a y + 7 = 0
L3: b x + 2 y + 5 = 0
L1 || L3 => the coefficients of x and y in L1 and L2 are proportional or, the slopes of the two lines are equal.
3 : b = 1 : 2 => b = 6
L1 Perpendicular to L2. The product of the slopes is -1.
-3 * 1/a = -1 => a = 3
L2: x - a y + 7 = 0
L3: b x + 2 y + 5 = 0
L1 || L3 => the coefficients of x and y in L1 and L2 are proportional or, the slopes of the two lines are equal.
3 : b = 1 : 2 => b = 6
L1 Perpendicular to L2. The product of the slopes is -1.
-3 * 1/a = -1 => a = 3
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