Vectors And Cartesian Three-Space Practice Test
If necessary, review:
- Taste of Trigonometry Help
- Vectors in the Cartesian Plane Help
- 3D Coordinates Help
- Vectors in 3D Space Help
- Planes in 3D Space Help
- Lines in 3D Space Help
Vectors and Catesian Three-Space Practice Test
Directions: A good score is eight correct.
1. The dot product (3,5,0) • (−4,−6,2) is equal to
(a) the scalar quantity −4
(b) the vector (−12,−30,0)
(c) the scalar quantity −42
(d) a vector perpendicular to the plane containing them both
2. What does the graph of the equation y = 3 look like in Cartesian three-space?
(a) A plane perpendicular to the y axis
(b) A plane parallel to the xy plane
(c) A line parallel to the y axis
(d) A line parallel to the xy plane
3. Suppose vector d in the Cartesian plane begins at exactly (1,1) and ends at exactly (4,0). What is dir d , expressed to the nearest degree?
4. Suppose a line is represented by the equation ( x − 3)/2 = ( y + 4)/5 = z − 1. Which of the following is a point on this line?
(d) There is no way to determine such a point without more information
5. Let Δ PQR be a right triangle whose hypotenuse measures exactly 1 unit in length, and whose other two sides measure p meters and q meters, as shown in Fig. 9-14. Let θ be the angle whose apex is point P . Which of the following statements is true?
(a) sin θ = p/q
(b) sin θ = cos φ
(c) tan φ = tan θ
(d) cos θ = 1/(tan φ )
6. With reference to Fig. 9-14, the Pythagorean theorem can be used to demonstrate that
(a) sin θ + cos φ = 1
(b) tan θ − tan φ = 1
(c) (sin θ ) 2 + (cos θ ) 2 = 1
(d) (sin θ ) 2 − (cos θ ) 2 = 1
7. What is the cross product (2 i + 0 j + 0 k ) × (0 i + 2 j + 0 k )?
(a) 0 i + 0 j + 0 k
(b) 2 i + 2 j + 0 k
(c) 0 i + 0 j + 4 k
(d) The scalar 0
8. What is the sum of the two vectors (3,5) and (−5,−3)?
9. If a straight line in Cartesian three-space has direction defined by m = 0 i + 0 j + 3 k , we can surmise
(a) that the line is parallel to the x axis
(b) that the line lies in the yz plane
(c) that the line lies in the xy plane
(d) none of the above
10. Suppose a plane passes through the origin, and a vector normal to the plane is represented by 4 i − 5 j + 8 k . The equation of this plane is
(a) 4 x − 5 y + 8 z = 0
(b) −4 x + 5 y − 8 z = 7
(c) ( x − 4) = ( y + 5) = ( z − 8)
(d) impossible to determine without more information
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