I"m trying to do homework for my physics class, and also it claims I should find "the component of $veca$ along the direction of $vecb$". The vectors are:

$veca = 7.1hat ns + 8.97 hat j $

$vecb = 5.8hat ns + 2.5hat j$

I know exactly how to discover the $x$ and also $y$ components yet I"ve never done this before. How do I perform it?





Using the formula

$$ extcomp_b a = fraca cdot bvert b vert$$

with the offered vectors

$$veca = $$ $$vecb = $$ we get that

$$acdot b = cdot = (7.1cdot 5.8) + (8.9cdot 2.5) = 63.43$$

Then $$vert bvert = sqrt5.8^2 + 2.5^2 = sqrt33.64 + 6.25= sqrt39.89$$

Therefore the price is $$frac63.43sqrt39.89$$


I think the ingredient of A along B should be a vector. The ahead answer offers the size of the ingredient of A along B. Currently that need to be multiplied by a unit vector in the direction that B. So my answer would certainly be:

$comp_bA = frac A cdot B$ multiply by the vector $frac B$ we get $frac A cdot B B = frac A cdot BB cdot B B$

Then to acquire the component of A perpendicular come B, friend subtract that from A.

You are watching: Component of vector along another vector

Hint: the ingredient of $a$ follow me $b$ (also recognized as the scalar forecast of $a$ ~ above $b$) is provided by

$$ extcomp_b a = fraca cdot bvert b vert$$

where $a cdot b$ is the dot product.

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