Questions: The figure shows a rectangular box in three-dimensional space that contains several vectors. (The vector c is in the xz-plane, and the vector e is in the xy-plane.) Are the following statements true or false? 1. d = g - c 2. g = f + a 3. a = -b 4. c = f 5. a = d 6. e = a - b

Solution Steps

Vector d starts at the origin and ends at the same point as the tail of vector c. Vector g starts at the origin and ends at the same point as the head of vector c. Therefore, vector c + vector d = vector g. Rearranging, vector d = vector g - vector c.

Vector g starts at the origin and ends at the corner formed by vectors f and a. Vector f starts at the origin and aligns with the y-axis. Vector a is parallel to the z-axis. The vector sum f + a results in a vector equivalent to g.

Vector a is oriented in the positive z direction and vector b is oriented in the positive z direction. Thus, vector b = vector a, and it is not true that a = -b.

Final Answer: