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.
Answer – A letter
In algebraic equations, a variable refers to an unknown or changeable number. Typically, all the letters in the alphabet are used to represent variables in algebra. Letters from the Greek alphabet are also used in some advanced algebra. Therefore, in algebra, we use a letter to represent a variable.
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Answer:
8π
Step-by-step explanation:
360° = 2πr = πd
120° = 1/3 * 360°
120° = 2/3πr = 1/3πd
If the radius r = 12:
arcAB = 2/3π * 12 = 8π
Answer:
Step-by-step explanation:
<u>Given</u>
<u>Cross multiply and solve for x:</u>