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 a?

Question

1714 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-28T02:52:39

The magnitude (length) of a vector in two dimensions is given by:

$l=sqrt(a^2+b^2)$ . In this case, for the vector $a$ , $l=sqrt(3.3^2+(-6.4)^2) = sqrt(51.85)=7.2 units.$

To find the length of a vector in two dimensions, if the coefficients are $a$ and $b$ , we use:

$l=sqrt(a^2+b^2)$

This might be vectors of the form $(ax+by) or (ai+bj) or (a,b)$ .

Interesting side note: for a vector in 3 dimensions, e.g. $(ax+by+cz)$ , it's

$l=sqrt(a^2+b^2+c^2)$ - still a square root, not a cube root.

In this case, the coefficients are $a=3.3$ and $b=-6.4$ (note the sign), so:

$l=sqrt(3.3^2+(-6.4)^2) = sqrt(51.85)=7.2$ $units$