Question

Let $\mathbf{| \mathbf{a} |} = 5$ and $-2 \leq z \leq 1$. Then, the range of $|\mathbf{a}|$ is:

• A. $[5, 10]$
• B. $[-2, 5]$
• C. $[2, 1]$
• D. $[-10, 5]$

Hint:

To find the magnitude range of a vector, use the formula and check the given constraints.

Answer 1

The Correct Option is A

Given that $|\mathbf{a}| = 5$ and $-2 \leq z \leq 1$, the magnitude of vector $\mathbf{a}$ is 5. The magnitude of a vector is a scalar value. The range of possible magnitudes for this vector is determined by the values of $z$. Consequently, the vector's magnitude is within the interval $[5, 10]$.