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MA 1111: Linear Algebra I Tutorial problems, September 20, 2018

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MA 1111: Linear Algebra I Tutorial problems, September 20, 2018

1.Given that the points (1, 1), (−1,−1), and (0, 2) are three vertices of a parallelogram, find possible positions of its fourth vertex.

2.Compute the angle between the vectors a= (3, 5) and b= (2, 1).

3.(a) Compute the area of the parallelogram determined by the vectors u = (1, 2, 2)andv= (2, 3, 5). (b) Compute the volume of the parallelepiped determined by the vectors u= (1, 2, 2),v= (2, 3, 5), andw= (3, 0, 1).

4.Ifu,v, andware three-dimensional vectors, is the expressionu×(v·w) defined? Explain your answer.

5. (a) For a cube with side length equal to 1, show that only possible distances between its two vertices are 1, √

2, and √

3. (b) Take one ver- tex of a cube, say A, and connect it to two vertices B and C for which AB=AC=√

2. Determine the angle ∠BAC.

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