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>
Answer:
a
Step-by-step explanation:
Answer:
42cm^3
Step-by-step explanation:
Given data
Area of base= 14 square centimeters,
Height= 3 centimeters
Volume = Area* Height
Volume= 14*3
Volume= 42 cm^3
Hence the volume of the prism is 42cm^3
By applying Pythagorean theorem, we have proven that the point (-1/2, -√3/2) lies on the unit circle.
<h3>How to prove this point lies on the unit circle?</h3>
In Trigonometry, an angle with a magnitude of -120° is found in the third quarter and as such, both x and y would be negative. Also, we would calculate the reference angle for θ in third quarter as follows:
Reference angle = 180 - θ
Reference angle = 180 - 120
Reference angle = 60°.
For the coordinates, we have:
sin(-120) = -sin(60) = -1/2.
cos(-120) = -cos(60) = -√3/2.
By applying Pythagorean theorem, we have:
z² = x² + y²
z = √((-1/2)² + (-√3/2)²)
z = √(1/4 + 3/4)
z = √1
z = 1.
Read more on unit circle here: brainly.com/question/9797740
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