Answer:
Explanation:
Generally, length of vector means the magnitude of the vector.
So, given a vector
R = a•i + b•j + c•k
Then, it magnitude can be caused using
|R|= √(a²+b²+c²)
So, applying this to each of the vector given.
(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 means 1k
The length is
L = √(5²+(-2)²+1²)
Note that, -×- = +
L = √(25+4+1)
L = √30
L = 5.477 unit
(c) 2i − k
Note that, since there is no component j implies that 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
Same as above no is 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
If you do not have to use relative physics but classic physics, this is how you solve it:
Speed of light = c = 3 * 10^5 km/s
Speed of your foe respect to you: 0.259c
Speed of the torpedo respect to you: 0.349c
Speed of the torpedo respect your foe: 0.349c - 0.259c = 0.09c
Conversion to km/s = 0.09 * 3.0 * 10^5 km/s = 27000 km/s
Note that this solution, using classic physics do not take into account time and space dilation.
Answer: 27000 km/s
Waterfalls are created when a river flows following a descending rapid slope. The waterfall, then, flows from the source (where it starts) to the mouth (where it ends).
Waterfalls are created when the erosion of the rocks at the bottom of the slope is more powerful than the erosion of the rocks on the top.
After many years the water is able to erode the rocks on the top as well, and the waterfall slowly disappears.
Therefore the options that apply are:
b) waterfalls move towards their mouth;
c) the top or cap rock is resistant to erosion;
<span>f) waterfalls indicate a youthful river </span>
