Answer:
Explanation:
The length of a vector refers to its magnitude.
For a vector
R = a•i + b•j + c•k
The magnitude can be calculated using
|R|= √(a²+b²+c²)
Applying this formula to each given vector yields the following results.
(a) 2i + 4j + 3k
The length is
L = √(2²+4²+3²)
L = √(4+16+9)
L = √29
L = 5.385 unit
(b) 5i − 2j + k
Note that k represents 1k
The length is
L = √(5²+(-2)²+1²)
Because, -×- = +
L = √(25+4+1)
L = √30
L = 5.477 unit
(c) 2i − k
As there is no j component, it means that the j component is 0
L = 2i + 0j - 1k
The length is
L = √(2²+0²+(-1)²)
L = √(4+0+1)
L = √5
L = 2.236 unit
(d) 5i
Similarly, without a j-component and k-component
L = 5i + 0j + 0k
The length is
L = √(5²+0²+0²)
L = √(25+0+0)
L = √25
L = 5 unit
(e) 3i − 2j − k
The length is
L = √(3²+(-2)²+(-1)²)
L = √(9+4+1)
L = √14
L = 3.742 unit
(f) i + j + k
The length is
L = √(1²+1²+1²)
L = √(1+1+1)
L = √3
L = 1.7321 unit
Answer:
The output power of the circuit is 3 Watts.
Given:
a loss in decibels = 3 dB
Input power = 6 Watts
To find:
What is the output power?
Formula used:
Output power = Input power × loss in ratio
Solution:
3 dB loss corresponds to a ratio of 0.5
Output power can be calculated as follows:
Output power = Input power × loss in ratio
Output power = 6 × 0.5
Output power = 3 Watts
Therefore, the output power of the circuit is 3 Watts.
The required lift force is approximately 866.92 N. To determine this, we first establish the shark's mass at 92 kg and its density at 1040 kg/m³. The volume of the shark is calculated by dividing mass by density, yielding 0.08846 m³. The buoyant force acting on the shark is then determined by multiplying the volume by the density of water and gravity, resulting in a lift force of 866.92 N.
Kinetic energy refers to the energy an object possesses while in motion, whereas thermal energy corresponds to heat energy. In situations where heat increases in materials, such as a solid turning into a liquid, the molecules start to move more rapidly, resulting in a rise in kinetic energy.
Explanation:
It is stated that,
Area of square coil, 
Length of one side of the square, L = 0.02 m
Number of coils, N = 10000
Consistent magnetic field, B = 1.5 T
Velocity, v = 100 m/s
An electromotive force is produced in the coil calculated as:
E = 30000 V
Breakdown voltage of air, 
Let d be the distance between the ends of the coil wires that can still produce a spark. Therefore,
Electric field, 
d = 0.075 m
Thus, this forms the final answer.
