On a plane flat surface with "up" given as +y and "right" given as +x, we add two vectors. One of them has components (3, 4) and the other is (-1,-4). What is the length of the resulting vector, and what direction is it pointing in? O The vector has length of 4 and it is in the positive x directon. The vector has length of 12 and is pointing up and to the right at 45°. O The vector has length of 1 and is pointing up and to the left at 45°. O The vector has length of 2 in the positive x direction.

Let vector A  point from the origin into the second quadrant of the xy plane and vector B point from the origin into the fourth quadrant. The vector B −A  must be in which quadrant?

In the next sets, you are given the magnitude and one component. There is an ambiguity in determining the vector, because you can only determine the absolute value of the other component and not its sign; therefore, there are two possibilities. In these tables, you must enter the absolute value of the component and provide two angles for the vector, the first one assuming the other component is positive and the other assuming the component is negative. You must also provide two angles for the antiparallel vector in the same order. Set Set 5a 5b 6a 6b Ax Axl 32 -26 X Ayl 53.1 56.28 Ay 42 -21 ✓ ✓ Magnitude of A 62 62 Magnitude of A 72 64 Angle of A 58.93 301.07 114.8 245.2 Angle of A Angle of -A ✔ (pos Ay) 238.93 ✓(neg Ay) 121.07 ° ✔ (pos A,) 294.8 ✓(neg Ay) 65.2 X X (pos Ax) (neg A,) (pos Ax) (neg Ax) Angle of -A ✓(pos Ay) ✔(neg Ay) ✔° (pos Ay) (neg Ay) X (pos A) X(neg Ax) (pos Ax) (neg A₂)

Consider vector A, with a magnitude of 3, and a vector B, with a magnitude of 2. Are the following relationships possible? If so, sketch a picture that shows an example of how they're possible, and identify all the angles between the vectors that make the relationship possible. (Exact angles, not decimal approximations. No calculators.) Relationship: Possible? Sketch: Angles: a. 1A+삐>5 b. A+ B| = 5 c. A+ B| = 1 d. A+미<1 - 1<|A+삐<5