SOLUTION: Suppose that vectors [a, b] and [c, d] are perpendicular. Show that ac + bd = 0.

Question 1073780: Suppose that vectors [a, b] and [c, d] are perpendicular. Show that ac + bd = 0.
Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!

The vector < a,b > when placed with tail at the origin 
(0,0) and tip at point (a,b) has slope: 



Similarly, The vector < c,d > when placed with tail at 
the origin (0,0) and tip at point (c,d) has slope: 



Since they are given to be perpendicular, their slopes
and opposite signed reciprocals.

Thus .

Multiply both sides by ad





Edwin

RELATED QUESTIONS
If a:b :: c:d, show that: ac : bd =... (answered by robertb)

email: maplespots@gmail.com Please help me solve this; "Quadrilateral ABCD is a (answered by solver91311)

Three vectors a,b and c are such that a.(b+c)=b.(a+c) Show that c must be... (answered by jim_thompson5910)

A triangle is right- angled at B. D is the point on AC such that BD is perpendicular to... (answered by mananth)

show that the vectors a=2i+3j-k and b=3i-j+3k are... (answered by Alan3354)

Find the slope of AC and BD. Decide whether AC is perpendicular to BD. A(-1,-2) B(-3,2)... (answered by mananth)

Suppose that {{{a^2 + b^2=1}}} and {{{c^2 + d^2=1}}}. Prove: {{{abs(ac + bd)<= 1}}}.... (answered by Edwin McCravy)

Suppose a, b, c are all real numbers such that a+b+c > 0; abc > 0 and ab+bc+ac > 0: Show (answered by Edwin McCravy)

1. If A, B, C, D are collinear and AB = 8, AC = 12, AD = 16, BC = 20, BD = 24, CD = 28,... (answered by ikleyn)