MATH115 GEOMETRY AND CALCULUS
Workshop Exercises 1
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1.
Let , and .
i) Compute .
ii) Compute .
iii) Find a unit vector (i.e., a vector of length 1) which is orthogonal to both and .
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2.
Let , be vectors in .
i) Show that if then .
ii) Show that .
iii) Show that .
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3.
True or false?
i) There exist vectors and in such that .
ii) If then .
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4.
In each of the following cases, find , where is the angle between and .
i) , ,
ii) , ,
iii) , .
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5.
i) Find the equation of the line in which passes through the points and .
ii) Find the equation of the plane in with normal vector and which passes through the point .
iii) Find an equation describing the line in passing through the points and .