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?

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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#