Answer:
θ = Cos⁻¹[A.B/|A||B|]
A. The angle between two nonzero vectors can be found by first dividing the dot product of the two vectors by the product of the two vectors' magnitudes. Then taking the inverse cosine of the result
Explanation:
We can use the formula of the dot product, in order to find the angle between two non-zero vectors. The formula of dot product between two non-zero vectors is written a follows:
A.B = |A||B| Cosθ
where,
A = 1st Non-Zero Vector
B = 2nd Non-Zero Vector
|A| = Magnitude of Vector A
|B| = Magnitude of Vector B
θ = Angle between vector A and B
Therefore,
Cos θ = A.B/|A||B|
<u>θ = Cos⁻¹[A.B/|A||B|]</u>
Hence, the correct answer will be:
<u>A. The angle between two nonzero vectors can be found by first dividing the dot product of the two vectors by the product of the two vectors' magnitudes. Then taking the inverse cosine of the result</u>
Answer:
(-8.089 km, 3.945 km)
Explanation:
We need to find the x- and y-components of the following vector :
d (9 km, 26 degrees left of +y axis)
We know that the x and y component of any vector is given by :
So, x component :
y component :
So, the x and y components of the vector separated by a comma are (-8.089 km, 3.945 km). Hence, this is the required solution.
Answer:
W_net = mg + 2mgh/r
Explanation:
The forces applied in this motion of the bowling ball are both gravitational and centripetal forces.
Now, gravitational force is; F_g = mg
While centripetal force is; F_c = mv²/r
Since we want to express the net force in terms of the variables in the statement and we are not given "v", let's find an expression of v with the variables given.
Now, from Newton's equation of motion, at initial velocity of 0, v² = 2gh.
Thus;
F_c = 2mgh/r
Where;
m is ball mass
r is tube radius
h is fall height
Thus, the net force will be;
F_net = F_g + F_c
Now, Net force would be equal to the net weight that will be read on the scale.
Thus;
W_net = F_net = F_g + F_c
W_net = mg + 2mgh/r
Current in an electrical circuit can effectively be reduced to zero by inserting a very high resistance