Answer:
Let the vectors be
a = [0, 1, 2] and
b = [1, -2, 3]
( 1 ) The cross product of a and b (a x b) is the vector that is perpendicular (orthogonal) to a and b.
Let the cross product be another vector c.
To find the cross product (c) of a and b, we have
![\left[\begin{array}{ccc}i&j&k\\0&1&2\\1&-2&3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Di%26j%26k%5C%5C0%261%262%5C%5C1%26-2%263%5Cend%7Barray%7D%5Cright%5D)
c = i(3 + 4) - j(0 - 2) + k(0 - 1)
c = 7i + 2j - k
c = [7, 2, -1]
( 2 ) Convert the orthogonal vector (c) to a unit vector using the formula:
c / | c |
Where | c | = √ (7)² + (2)² + (-1)² = 3√6
Therefore, the unit vector is
![\frac{[7,2,-1]}{3\sqrt{6} }](https://tex.z-dn.net/?f=%5Cfrac%7B%5B7%2C2%2C-1%5D%7D%7B3%5Csqrt%7B6%7D%20%7D)
or
[ 
, 
, 
]
The other unit vector which is also orthogonal to a and b is calculated by multiplying the first unit vector by -1. The result is as follows:
[ 
, 
, 
]
In conclusion, the two unit vectors are;
[ , , ]
and
[ , , ]
<em>Hope this helps!</em>
You originally start out with 28 marbles. each marble has a number out of 28 to create a percentage. 21/28 or 75% signifies red, 4/28 or about 14% is white and 3/28 or about 11% is gray. add white and gray, which is 7/28 combined or 25% together. multiply by number of times the process is completed, which is 112 and the final answer is 28
Answer:
x = 0
Step-by-step explanation:
8 + 6x = 4 * 2
If this is the equation then start with multiplying 4 by two and subtracting 8 from both sides
6x = 0
Divide 6 from both sides
x = 0
To test this, insert the value of x which is 0
8 + 6(0) = 4 * 2
Multiply 6 and 0
8 + 0 = 4 * 2
Multiply 4 and 2
8 + 0 = 8
Add
8 = 8
This equation is true as you can see so x is equal to 0.
Hope this helps.
- Que
