Find the area if the diameter is 14 mm
1 answer:
You might be interested in
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
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>
Answer:
The coordinates of the point b are:
b(x₂, y₂) = (-5, -1)
Step-by-step explanation:
Given
As m is the midpoint, so
m(x, y) = m (-7, -2.5)
The other point a is given by
a(x₁, y₁) = a(-9, -4)
To determine
We need to determine the coordinates of the point b
= ?
Using the midpoint formula
substituting (x, y) = (-7, -2.5), (x₁, y₁) = (-9, -4)
Thus equvating,
Determining the x-coordinate of b
[x₂ + (-9)] / 2 = -7
x₂ + (-9) = -14
x₂ - 9 = -14
adding 9 to both sides
x₂ - 9 + 9 = -14 + 9
x₂ = -5
Determining the y-coordinate of b
[y₂ + (-4)] / 2 = -2.5
y₂ + (-4) = -2.5(2)
y₂ - 4 = -5
adding 4 to both sides
y₂ - 4 + 4 = -5 + 4
y₂ = -1
Therefore, the coordinates of the point b are:
b(x₂, y₂) = (-5, -1)