MA 1004 D-95 Sample Exam 1 (with answers)

Show your work in the space provided. Unsupported answers may not receive full credit. Use the backs of the pages if needed. (On the real exam, there will be plenty of space for your work.)

1. If P is the point and Q is the point , find the vector .

   

2. If and compute the following quantities.
   1. 

      

   2. 

      

   3. .

      

   4. .

      

3. Determine whether the two vectors and are perpendicular. Explain your answer.

   Since and the two vectors are non-zero, they must be perpendicular.

4. If and , find , the vector component of in the direction of .

   

5. Use the properties of the dot and cross products to show that the following vector identity is true.

   

   

   since the dot product is distributive. Now,

   

   and

   

6. Find a vector parametric equation for the line through the point with direction vector .

   

7. Find an equation of the form Ax+By+Cz+D=0 for the plane through the three points , , and .

   

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