Question

Why is the product of the gradients of 2 straight line perpendicular to each other is always equal to -1 ?? Please prove it......?

Answer 1

m1=1/m2

you can use two rules (straight line) to prove it.

Answer 2

Give me a hint?

Answer 3

you can write equation of the lines perpedicular to each other in this form:
ax+by=0
-bx+ay=0
this is a hint....:)

Answer 4

Can you prove it through trigonometry?

Answer 5

@myko @shirleyx Can you prove it through trigonometry?

Answer 6

slope = \( \tan(\theta) \)
another slope = \( \tan(\theta - 90) = -\cot \theta \)

Answer 7

\[\cos \alpha x+\sin \alpha y =0\]
\[-\sin \alpha x + \cos \alpha y =0\]

Answer 8

grad f1 = (cosa -sinax,sina+cosay)
grad f2 = (-sina-cosax,cosa-sinay)