Question

Compute ∥v∥ for v=⟨0.1,0.5⟩. Use one decimal place.

Answer 1

The norm (or magnitude) of a vector v = ⟨0.1, 0.5⟩ is computed using the Euclidean norm formula:

Step-by-step explanation:

The norm or magnitude of the vector v=⟨0.1,0.5⟩ is calculated by squaring the components, adding them and taking the square root. The computed value, approximated to one decimal place, is 0.5. The given vector is v=⟨0.1,0.5⟩. The norm, or magnitude, of a vector v=⟨x,y⟩ is given by the formula ∥v∥ = sqrt(x² + y²). Here, x=0.1 and y=0.5.

To perform the calculation, we square both the x and y components, add them together, and then take the square root

So, ∥v∥ = sqrt((0.1)² + (0.5)²) = sqrt(0.01+0.25) = sqrt(0.26).

Approximating this to one decimal place, we get ∥v∥ = 0.5.

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