I want to find the vertical or you could say perpendicular component of a →...

Lisa Hardin

Lisa Hardin

Answered

2022-07-20

I want to find the vertical or you could say perpendicular component of a on b
Now I know that it can be found out using a ( a b | b | ) b
However I wanted to know why it cannot be found out using this method I tried. What is the flaw in it?
a × b = | a | | b | sin θ n ^ Now n ^ should be equal to ( a × b ) | a × b |
Using this I can write the expression as a × b = | a | | b | sin θ × ( a × b ) | a × b | which on simplifying gives me
| a × b | | b | = | a | sin θ which I believe should be the perpendicular component
Now I'm probably doing something really stupid but I can't really understand where am I going wrong ?

Answer & Explanation

fairymischiefv9

fairymischiefv9

Expert

2022-07-21Added 11 answers

You are correct that the maginitude of the transverse component of a relative to the direction b ^ = b / | b | is given by | a × b ^ | for R 3 . However, this does not tell you the direction of of the transverse component.
It's direction is not along n ^ , a n ^ = 0; it's direction is along n ^ × b ^
Of course, all of this cross-product stuff only works in 3 dimensions.

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