Answer:
Step-by-step explanation:
Given:
u = 1, 0, -4
In unit vector notation,
u = i + 0j - 4k
Now, to get all unit vectors that are orthogonal to vector u, remember that two vectors are orthogonal if their dot product is zero.
If v = v₁ i + v₂ j + v₃ k is one of those vectors that are orthogonal to u, then
u. v = 0 [<em>substitute for the values of u and v</em>]
=> (i + 0j - 4k) . (v₁ i + v₂ j + v₃ k) = 0 [<em>simplify</em>]
=> v₁ + 0 - 4v₃ = 0
=> v₁ = 4v₃
Plug in the value of v₁ = 4v₃ into vector v as follows
v = 4v₃ i + v₂ j + v₃ k -------------(i)
Equation (i) is the generalized form of all vectors that will be orthogonal to vector u
Now,
Get the generalized unit vector by dividing the equation (i) by the magnitude of the generalized vector form. i.e
Where;
|v| = 
|v| = 
= 
This is the general form of all unit vectors that are orthogonal to vector u
where v₂ and v₃ are non-zero arbitrary real numbers.
Answer: 
Step-by-step explanation:
Lines perpendicular to another line have inversely proportional slopes. We are given that the slope of the line is -4, so the slope of the perpendicular line will be positive 1/4. Now we have a starting point for this line:
Notice how I plugged in the points given.
Increasing the number of traffic lights on the most used route between the two destinations will increase the amount of time it will take to reach to the other destination, as each traffic light will cause a delay. Therefore, the increasing number of traffic lights are causing an increase in the average time to travel to the other destination.
In this case the correlation is most likely a casuation as the increase in the number of traffic lights is causing an increase in the average driving time between the two destinations.
So, the correct answer is option B
Answer:
4
Step-by-step explanation:
Answer:
x = 45 and y = 90
Step-by-step explanation:
Let the third angle be z
z = 180 - 135 (Linear Pair)
z = 45
Since its an iscosceles triangle,
<z = <x (angles opposite to equal sides have equal angles)
<x = 45 degree
<z + <x + <y = 180
45 + 45+ <y = 180
90 + <y = 180
<y = 180 - 90
<y = 90
Therefore x = 45 and y = 90
Hope u understood please mark as brainliest
Thank You
