How does multiplying a vector by a scalar value of -pi/4 change the vector?
A.) The vector will change direction and increase in magnitude.
B.) The vector will change direction and decrease in magnitude.
C.) The vector will not change direction but will increase in magnitude.
D.) The vector will not change direction but will decrease in magnitude.
Unit 5 Lesson 8: 5/13/2022
1. The vector will change direction and decrease in magnitude.
2. 56 ft lbs.
3.(-3,-2)
4. u= -5sqrt29/29i - -2sqrt29/29j
5. 56
6.11.4 ft./sec.
7. Written... equal on directions and magnitude.
8. (-10, -16)
8B. 2sqrt89
9. (-14, -21)
9B. 7sqrt13
10. (-18,-26)
10B. 10sqrt10
11. 5, 144 degrees
12. 173 degrees
13. (1/6, -1/5)
14. 159 mph
15. 10j
16. 2sqrt6
17. 98.4 degrees
18. written= dot concept and answer if 26.56 degrees.
warning the mix up the questions they arnt always the same
B. The direction will change 180o, and the magnitude will decrease.
I'm assuming you mean -pi/4.
Well, well, well, let's see what we have here. Multiplying a vector by a negative value of -pi/4 is like giving it a little spin on the dance floor. So, which option could it be?
A.) The vector will change direction and increase in magnitude. Hmmm, sounds like the vector is busting a move and trying to be the center of attention. But is that what happens here? Let's keep going.
B.) The vector will change direction and decrease in magnitude. Ah, now this option sounds like the vector is getting a bit shy and dialing down its moves. Could this be the answer?
C.) The vector will not change direction but will increase in magnitude. Hmm, no change in direction but somehow it's getting bigger? Maybe it's been eating too many vector snacks lately. Interesting.
D.) The vector will not change direction but will decrease in magnitude. Ah, now this option sounds like the vector is losing its confidence and shrinking back into its shell. Is that the case?
Okay, drum roll, please! The correct answer is B - the vector will change direction and decrease in magnitude. It's like getting a little dizzy, doing a half pirouette, and shrinking at the same time. Keep those vectors on their toes!
To determine how multiplying a vector by a scalar value of -π/4 changes the vector, we need to understand what it means to multiply a vector by a scalar.
When you multiply a vector by a scalar, you are essentially scaling the vector by that scalar. The scalar value determines the magnitude of the resulting vector, and it can also determine the direction if the scalar is negative.
In this case, the scalar value is -π/4, which means we'll be scaling the vector negatively by π/4 radians.
Since the scalar is negative, it will change the direction of the vector. In other words, the resulting vector will be in the opposite direction of the original vector.
Furthermore, since the scalar value is less than 1 (π/4 < 1), the magnitude of the resulting vector will be smaller than the magnitude of the original vector.
So, the correct answer is:
D.) The vector will not change direction but will decrease in magnitude.