Two vectors are given by a = 3.3 x - 6.4 y and b = -17.8 x + 5.1 y. What is the magnitude of the vector a + b?

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Two vectors are given by a = 3.3 x - 6.4 y and b = -17.8 x + 5.1 y. What is the magnitude of the vector a + b?

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Answer 1 · 2016-04-02T12:39:37

$|a + b| = 14.6$

Explanation:

Split up the two vectors into their $x$ and $y$ components and add them to their corresponding $x$ 's or $y$ 's, like so:

$3.3x + -17.8x = -14.5x$
$-6.4y + 5.1y = -1.3y$

Which gives a resultant vector of $-14.5x - 1.3y$

To find the magnitude of this vector, use Pythagoras theorem. You can imagine the $x$ and $y$ components as perpendicular vectors, with a right angle where they join, and the $a + b$ vector, let's call it $c$ , joining the two, and so $c$ is given by:

$c^2 = x^2 + y^2$
$c = sqrt(x^2 + y^2)$

Substituting the values of $x$ and $y$ ,

$c = sqrt(211.9)$
$c = 14.6$

which is the magnitude or length of the resultant vector.

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Two vectors are given by a = 3.3 x - 6.4 y and b = -17.8 x + 5.1 y. What is the magnitude of the vector a + b?

1 Answer

Explanation:

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