Find the angles which the vecotr <span><span><span><span><span>v </span><span>⃗ </span></span>=3i−6j+2k</span> </span><span><span>v→</span>=3i−6j+2k</span></span>
makes with the coordinate axes.
If the angles are <span><span><span>α,β,θ</span> </span><span>α,β,θ</span></span>
, show that for any 3-dimensional vector:
. . . <span><span><span><span><span>cos </span><span>2 </span></span>α+co<span><span>s </span><span>2 </span></span>β+<span><span>cos </span><span>2 </span></span>θ=1</span> </span><span><span>cos2</span>α+co<span>s2</span>β+<span>cos2</span>θ=1</span></span>
The last one, the soil will become weak & unable to support plant growth
Answer:
Speed: 4.8 m/s
Velocity: 4.8 m/s north
Explanation:
Definitions:
- Speed is a scalar quantity, which is equal to the ratio between distance covered (d) and time taken (t):

- Velocity is a vector quantity, whose magnitude is equal to the ratio between the displacement of the object and the time taken:

And it also has a direction (the same as the displacement).
In this problem:
- The object travels a distance of
d = 105 m
In a time interval of
t = 22 s
So its speed is

- The displacement of the object is the same as the distance in this case, so still 105 m, covered in a time interval of 22 s; this means that the magnitude of the velocity is the same as the speed:

However, velocity is a vector quantity, so it also has a direction: and since the object has moved north, the direction of the velocity is north as well.
Answer:
Induced emf in the loop is 0.02208 volt.
Induced current in the loop is 0.0368 A.
Explanation:
Given that,
Area of the single loop, 
The initial value of uniform magnetic field, B = 3.8 T
The magnetic field is decreasing at a constant rate, 
(a) The induced emf in the loop is given by the rate of change of magnetic flux.

(b) Resistance of the loop is 0.6 ohms. Let I is the current induced in the loop. Using Ohm's law :

Hence, this is the required solution.
F=ma so a=F/m
a=225/55=4.09 m/sec^2