Respuesta :

Write the two vectors as
[tex]\vec{a} =4\vec{i} + 4\vec{j}[/tex]
[tex]\vec{b} = -7\vec{i}+3\vec{j}[/tex]

By definition, the projection of [tex]\vec{a}[/tex] onto [tex]\vec{b}[/tex] is
[tex]a_{b} = \vec{a} . \frac{\vec{b}}{|b|} [/tex]

[tex]\hat{b} = \frac{\vec{b}}{|b|} = \frac{1}{\sqrt{49+9}} (-7\vec{i}+3\vec{j})=(-7\vec{i}+3\vec{j})/\sqrt{58}[/tex]

Therefore
[tex]\vec{a} . \vec{b} = -28+12=-16[/tex]
[tex]a_{b} = -16/\sqrt{58} = -2.1[/tex]

Answer:
The projection of (4 4) onto (-7 3) is -2.1.

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