Explanation

x =  \(\begin{pmatrix} -4 \\ 3 \end{pmatrix}\) and y= \(\begin{pmatrix} -9 \\ 15 \end{pmatrix}\)

Changing x and y to the form xi+yj

we have x= -4i + 3j and y = -9i - 15j

using cosØ = \(\frac{xy}{|x|ly|}\)

where Ø is the angle between x and y

xy = (-4i+3j) (-9i - 15j)

-36 + 60 x 0 - 27 x 0- 45 = -81

|x| = √(4\(^2\) +3\(^2\)) =√(16 +9) = √25 = 5

|y| = √(-9)\(^2\) + (-15)\(^2\) = √(81 +225) = √306

cosØ =\(\frac{-81}{5√306}\)

= \(\frac{-9√306}{170}\)

\(\frac{17.49 * 9}{170}\)

Ø = cos\(^{-1}\)(-0.1029);

Ø = 95.91°

Ø = 96°

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