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

Suppose that ac + bd = 0. Show that vectors [a, b] and [c, d] are perpendicular. The number ac + bd is called the dot product of the vectors [a, b] and [c, d].

Solutions

Expert Solution

Solution 1 :-

Here we're given ac+bd = 0

And we also know that ac+bd is the dot product of the vectors [a, b] and [c, d]

Thus dot product of the vectors [a, b] and [c, d] is 0.

By equation, dot product of two vectors m and n = |m|*|n|*cos

So cos = 0 when dot product is 0.

cos =0 implies angle between vectors is 90In short, ^*=0 ⟹ cosθ=0 ⟹ θ=90

Hence vectors [a, b] and [c, d] are perpendicular.

Solution 2 :-

Just demonstrating another approach to show that two vectors are perpendicular

That is the slopes of vectors are opposite signed reciprocals. This implies that the vectors are perpendicular.

Hope my solution helps you. Kindly rate if it is helpful.

milcah answered 1 year ago

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