Let v be a vector with initial point (-5, -11) and terminal point (6, 2). What is the norm of vector v?
Answer (2)
The norm of vector v, defined from initial point (-5, -11) to terminal point (6, 2), is calculated as 290 , which approximates to 17.03. This is found by determining the vector components and applying the norm formula. Thus, the norm represents the length of the vector in space.
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To find the norm of a vector v with initial point ( − 5 , − 11 ) and terminal point ( 6 , 2 ) , we first need to determine the vector's components.
The vector v can be expressed in component form as follows:
v = ( x 2 − x 1 , y 2 − y 1 )
where ( x 1 , y 1 ) is the initial point and ( x 2 , y 2 ) is the terminal point.
Substituting the points into the equation gives:
v = ( 6 − ( − 5 ) , 2 − ( − 11 ))
This simplifies to:
v = ( 6 + 5 , 2 + 11 ) = ( 11 , 13 )
The norm or magnitude of the vector v , denoted as ∣∣ v ∣∣ , is determined by the formula:
∣∣ v ∣∣ = x 2 + y 2
Applying the components of v , we have:
∣∣ v ∣∣ = 1 1 2 + 1 3 2
Calculating the squares gives:
∣∣ v ∣∣ = 121 + 169
Adding the values:
∣∣ v ∣∣ = 290
Approximating the square root:
∣∣ v ∣∣ ≈ 17.03
Thus, the norm of the vector v is approximately 17.03 . This is the length or magnitude of the vector from the initial point to the terminal point.
