91Ó°ÊÓ

A wind is blowing due west at \(60 \mathrm{km} / \mathrm{h}\). A small plane with air speed of \(300 \mathrm{km} / \mathrm{h}\) is trying to maintain a course due north. In what direction should the pilot steer the plane to keep the targeted course? How fast is the plane moving?

Write (4,7) as a linear combination of (2,3) and (2,1)

Note: \(\left(\begin{array}{l}8 \\ 46\end{array}\right)\) is said to be written as a linear combination of \(\left(\begin{array}{l}1 \\ 9\end{array}\right)\) and \(\left(\begin{array}{c}1 \\ -4\end{array}\right)\) Write (4,7) as a linear combination of (2,3) and (2,1).

The points \(P(2,2), Q(10,2)\) and \(R(12,6)\) are three vertices of a parallelogram. Find the fourth vertex \(S\) if a) \(P\) and \(R\) are vertices of the same diagonal b) \(P\) and \(R\) are vertices of a common side.

Write (5,-5) as a linear combination of (1,-1) and (-1,1).

Note: \(\left(\begin{array}{l}8 \\ 46\end{array}\right)\) is said to be written as a linear combination of \(\left(\begin{array}{l}1 \\ 9\end{array}\right)\) and \(\left(\begin{array}{c}1 \\ -4\end{array}\right)\) Write (5,-5) as a linear combination of (1,-1) and (-1,1).

Show, using vector operations, that the diagonals of a parallelogram intersect each other.

Write (-11,0) as a linear combination of (2,5) and (3,2)

Note: \(\left(\begin{array}{l}8 \\ 46\end{array}\right)\) is said to be written as a linear combination of \(\left(\begin{array}{l}1 \\ 9\end{array}\right)\) and \(\left(\begin{array}{c}1 \\ -4\end{array}\right)\) Write (-11,0) as a linear combination of (2,5) and (3,2)

Show, using vector operations, that the line segment joining the midpoints of two sides of a triangle is parallel to the third side and has half its length.