Question

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?

Answer 1

`|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.