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
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>
To find the GCF:
-- List the factors of the first number.
-- List the factors of the second number.
-- Make a short list of the factors that show up for BOTH numbers.
-- Find the biggest number on the short list.
Factors of the first number (99): <u>1</u>, 3, 9, <u>11</u>, 33, 99 .
Factors of the second number (121): <u>1</u>, <u>11</u>, 121 .
Short list (factors that show up for both numbers): 1, 11
Biggest number on the short list: <em>11</em>
9514 1404 393
Answer:
y = 2
Step-by-step explanation:
The variable x can be eliminated by subtracting the first equation from the second.
(-x +4y) -(-x -y) = (15) -(5)
5y = 10 . . . . . . . simplify
y = 2 . . . . . . . . . divide by 5