Question

If a vector A has components A. 0, and Ay -0, then the magnitude of the vector is negative. Select one: True False

Answer 1

Answer:

False

Explanation:

The magnitude of any vector is given by,

$||A||=\sqrt{A_x^2+A_y^2}$

The magnitude of anything is never negative. It can be even seen from the formula that the components are squared. A squared value can never be negative. Even if the component is negative the square will be always positive.

So, magnitude of the vector is not negative.

Answer 2

Answer:

The given statement is false.

Explanation:

For a given vector $\overrightarrow{A}=A_{x}\widehat{i}+A_{y}\widehat{j}$

The magnitude is given by $|A|=\sqrt{A_{x}^{2}+A_{y}^{2}}$

As we can see that the quantity on the right side of equation is always positive since square root of a quantity is always positive thus we conclude that the magnitude of any vector and hence vector A is always positive.