Answer:
one unit vector is ur=(-1/√3 ,1/√3 ,1/√3 )
Step-by-step explanation:
first we need to find a vector that is ortogonal to u and v . This vector r can be generated through the vectorial product of u and v , u X v :![r=u X v =\left[\begin{array}{ccc}i&j&k\\1&0&1\\0&1&1\end{array}\right] = \left[\begin{array}{ccc}0&1\\1&1\end{array}\right]*i + \left[\begin{array}{ccc}1&0\\1&1\end{array}\right]*j + \left[\begin{array}{ccc}1&0\\0&1\end{array}\right]*k = -1 * i + 1*j + 1*k = (-1,1,1)](https://tex.z-dn.net/?f=r%3Du%20X%20v%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Di%26j%26k%5C%5C1%260%261%5C%5C0%261%261%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%261%5C%5C1%261%5Cend%7Barray%7D%5Cright%5D%2Ai%20%2B%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%5C%5C1%261%5Cend%7Barray%7D%5Cright%5D%2Aj%20%2B%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%5C%5C0%261%5Cend%7Barray%7D%5Cright%5D%2Ak%20%3D%20-1%20%2A%20i%20%2B%201%2Aj%20%2B%201%2Ak%20%3D%20%28-1%2C1%2C1%29)
then the unit vector ur can be found through r and its modulus |r| :
ur=r/|r| = 1/[√[(-1)²+(1)²+(1)²]] * (-1,1,1)/√3 =(-1/√3 ,1/√3 ,1/√3 )
ur=(-1/√3 ,1/√3 ,1/√3 )
Answer:
y = 7x - 48
Step-by-step explanation:
To find the equation of the line
y = mx + c
Step 1 : find the slope
( 6, -6) ( 8, 8)
x_1 = 6
y_1 = -6
x_2 = 8
y_2 = 8
Insert the values into
m =( y_2 - y_1) /( x_2 - x_1)
m - slope
m = (8 - (-6)) / (8 -6 )
m = 8 +6 / 8 - 6
m = 14 / 2
m = 7
Step 2: substitute slope into intercept form equation
y = mx + c
y = 7x + c
Step 3: substitute either point into the equation in step 2
y = 7x + c
Let's pick point ( 8,8)
y = 8
x = 8
y = 7x + c
8 = 7(8) + c
8 = 56 + c
8 - 56 = c
c = 8 - 56
c = -48
Substitute the value of c back into the equation
y = 7x + c
y = 7x - 48
The equation of the line is
y = 7x - 48
The bottom one is correct.
Answer:
E looks like it is most congruent
Step-by-step explanation:
After entering in these systems in a graphing calculator under the y equals, you can determine that the lines are intersecting. They cross paths, so they cannot be parallel. The lines do not make a ninety-degree angle, so they are not perpendicular. This would make them intersecting.
