Let a &amp; b be non-zero vectors such that a ⋅ b = 0. Use geometric description of scalar product to show that a &amp; b are perpendicular vectors.What I've done so far is to state that cos ⁡ 90 (i.e. perpendicular) gives 0 which would make the rest of the equation | a | | b | cos ⁡ θ = 0

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Let a &amp;amp; b be non-zero vectors such that   a  ⋅  b  =  0. Use geometric description of scalar product to show that a &amp;amp; b are perpendicular vectors.What I&#039;ve done so far is to state that   cos  ⁡  90 (i.e. perpendicular) gives 0 which would make the rest of the equation       |    a      |        |    b      |    cos  ⁡  θ  =  0

Royce Golden · Accepted Answer

You have all the correct ideas. It&#039;s now about putting them together in a coherent way. You are told that   a  ⋅  b  =  0. You know that   a  ⋅  b  =      |    a      |        |    b      |    cos  ⁡  θ. Therefore,   0  =      |    a      |        |    b      |    cos  ⁡  θ. So one of       |    a      |    ,      |    b      |    ,  cos  ⁡  θ is zero. Use what was given about a,b to explain why |a|,|b| are not zero. Then have you know,   cos  ⁡  θ  =  0. Now   θ is the angle between a,b. Because   cos  ⁡  θ  =  0, what are the possibilities for   θ? What does this mean about a,b?

ghettoking6q · Accepted Answer

It is given that a and b are non-zero, and the dot product is zero. This means that      |    a      |        |    b      |    cos  ⁡  θ  =  0This means that one of the above factors is zero (null factor law). But we know that   a  ,  b  ≠  0, so the only way the above product is zero is if   cos  ⁡  θ  =  0, which implies that   θ  =  90      °  , and hence the two vectors are perpendicular

Let a & b be non-zero vectors such that a * b=0. Use geometric description of scalar product to show that a & b are perpendicular vectors.

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