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.
Lets call x the amount of 18% solution and y the amount of 40% solution, and write as equations the info of the problem:
18x + 40y = 10(20)
x + y = 10
lets multiply the second equation by -18 and add to the first:
18x + 40y = 200
-18x -<span> 18y = -180
</span>----------------------
0 + 22y = 20
y = 20/22 = 10/11
and substitute in the original equation:
x <span>+ y = 10
</span>x = 10 - y
x = 10 - 10/11
x = 110/11 - 10/11
x = 100/11
so they have to use 100/11 liters of 18% solution and 10/11 liters of 40% solution
V3+4v2-5v+3v2+12v-15
v3+7v2+7v-15
Answer:
8
Step-by-step explanation:
