The cross product of the normal vectors of two planes result in a vector parallel to the line of intersection of the two planes.
Corresponding normal vectors of the planes are
<5,-1,-6> and <1,1,1>
We calculate the cross product as a determinant of (i,j,k) and the normal products
i j k
5 -1 -6
1 1 1
=(-1*1-(-6)*1)i -(5*1-(-6)1)j+(5*1-(-1*1))k
=5i-11j+6k
=<5,-11,6>
Check orthogonality with normal vectors using scalar products
(should equal zero if orthogonal)
<5,-11,6>.<5,-1,-6>=25+11-36=0
<5,-11,6>.<1,1,1>=5-11+6=0
Therefore <5,-11,6> is a vector parallel to the line of intersection of the two given planes.
General Idea:
When we are given a point P(x, y) centered at origin with a scale factor of k, then the dilated point will be given by P' (kx, ky)
Applying the concept:
In the diagram given, the coordinate of C is (6, 3). Triangle ABC is being dilated with the center of dilation at the origin. The image of C, point C' has coordinates of (7.2, 3.6).
If C (x, y) centered at origin with a scale factor of k, then the dilated point will be given by C' (kx, ky)
We know
& 
Substituting 6 for x in the equation
, we get
.
Dividing 6 on both sides
Simplifying fractions on both sides
Point A from the diagram is (-3, 3)
x-coordinate of A' = 
y-coordinate of A' = 
Point A' is given by (-3.6, 3.6)
Conclusion:
<u>Scale factor of dilation is 1.2</u>
<u>The coordinates of point A' is (-3.6, 3.6)</u>
Answer:
36 + 16 √3
Explanation!
You would first need to simply the radical by breaking the radicand up into a product of known factors!
So the answer would be 36 + 16 √3
If you want decimal form here you go! :)
63.7128129211
Hope this helps you out!
Answer:
B
Step-by-step explanation:
6x + 30 + 4x = 10(x+3)
10x + 30 = 10x + 30
0 = 0
5x-x=-2-7
4x=-9
x=2/3 or x=-2/3
Since there are 2 answers, it is not one solution.