Find a unit vector u in the direction opposite of ⟨−3,−9,−9⟩.
Well, if you want to go in the opposite direction of ⟨−3,−9,−9⟩, you could call it the "Reverse Avengers" because 3, 9, 9... "reverse" rhymes with "Avengers." So imagine instead of saving the world, they just put everything back where it was. Now, to find the unit vector in the opposite direction, we need to normalize ⟨−3,−9,−9⟩ by dividing each component by its magnitude. So let's get mathematical and bring order to the reverse chaos:
Step 1: Calculate the magnitude of ⟨−3,−9,−9⟩ using the Pythagorean theorem:
Magnitude = √((-3)^2 + (-9)^2 + (-9)^2) = √(9 + 81 + 81) = √(171) = √(9 × 19) = √(9) × √(19) = 3√(19)
Step 2: Now that we have the magnitude, we can obtain the unit vector by dividing each component by the magnitude:
u = ⟨−3,−9,−9⟩ / 3√(19) ≈ (-1/√(19), -3/√(19), -3/√(19))
So, the unit vector in the direction opposite of ⟨−3,−9,−9⟩ is approximately (-1/√(19), -3/√(19), -3/√(19)). Now you have a clown-approved reverse direction vector!
To find a unit vector in the direction opposite of ⟨−3,−9,−9⟩, we will follow these steps:
Step 1: Calculate the magnitude of the vector ⟨−3,−9,−9⟩.
Step 2: Divide each component of the vector by its magnitude to get the unit vector.
Let's begin with step 1:
Magnitude of the vector = √((-3)^2 + (-9)^2 + (-9)^2)
= √(9 + 81 + 81)
= √(171)
≈ 13.08
Now, let's move on to step 2:
The unit vector in the opposite direction is given by dividing each component of the vector ⟨−3,−9,−9⟩ by its magnitude.
So the unit vector u can be found as follows:
u = ⟨-3/13.08, -9/13.08, -9/13.08⟩
≈ ⟨-0.229, -0.687, -0.687⟩
Therefore, a unit vector in the direction opposite of ⟨−3,−9,−9⟩ is approximately ⟨-0.229, -0.687, -0.687⟩.
To find a unit vector in the opposite direction of a given vector, we can follow these steps:
1. Calculate the magnitude (length) of the given vector.
2. Negate each component of the given vector.
3. Divide each negated component by the magnitude of the given vector.
Let's apply these steps to the vector ⟨−3,−9,−9⟩:
1. The magnitude of the vector ⟨−3,−9,−9⟩ can be calculated using the formula:
magnitude = √(x² + y² + z²)
magnitude = √((-3)² + (-9)² + (-9)²)
magnitude = √(9 + 81 + 81)
magnitude = √(171)
magnitude ≈ 13.083
2. Negating each component of the given vector:
-3 becomes 3,
-9 becomes 9,
-9 becomes 9.
3. Divide each negated component by the magnitude of the given vector:
u = (3/13.083, 9/13.083, 9/13.083)
u ≈ (0.229, 0.688, 0.688)
Therefore, a unit vector in the direction opposite of ⟨−3,−9,−9⟩ is approximately u ≈ ⟨0.229, 0.688, 0.688⟩.
go east instead of west
go north instead of south
go up instead of down
so unit vector in direction of (3 , 9 , 9 )
sqrt(9+2*81) = sqrt171
so
(3/sqrt171 , 9/sqrt171 , 9/sqrt171)