Aggarwal Abranshu

{eq}A=\sqrt{A_{x}^{2}+A_{y}^{2}} {/eq}

where {eq}A {/eq} is the magnitude of the vector, {eq}A_{x} {/eq} is the magnitude of the x-component, and {eq}A_{y} {/eq} is the magnitude of the y-component. All three variables must be in the same unit.

After calculating the magnitude of the vector we can use right triangle trigonometry to determine the angle the vector makes with the x-axis.

So, let's try using these steps to calculate the magnitude and direction of a vector in the following two examples!

Determine the magnitude and direction of vector {eq}A {/eq}.

Step 1: Use the equation {eq}A=\sqrt{A_{x}^{2}+A_{y}^{2}} {/eq} to calculate the magnitude of the vector.

From the figure, we can see that the x-component of the vector is {eq}85.8 {/eq} and the y-component of the vector is {eq}34.7 {/eq}. So we can say that {eq}A_x = 85.8 {/eq} and {eq}A_y = 34.7 {/eq}. Plugging these into the formula, we will have

$$\begin{align*} A&=\sqrt{85.8^{2}+34.7^{2}}\\ A &= 92.6 \end{align*} $$

Step 2: Use the equation {eq}\Theta =\tan^{-1}\left(\frac{A_{y}}{A_{x}} \right) {/eq} to calculate the direction of the vector.

Again, plugging in the values of {eq}A_x {/eq} and {eq}A_y {/eq} into the formula, we will have

$$\begin{align*} \Theta &=\tan^{-1}\left(\frac{34.7}{85.8} \right)\\ &= 22^{\circ} \end{align*} $$

Therefore, the magnitude of vector {eq}A {/eq} is {eq}92.6 {/eq} and its direction is {eq}\Theta =22^{\circ} {/eq}.

In May, Peloton issued a widespread recall for both of its treadmill machines, the Tread and the Tread+, after one child was killed in an accident and dozens of other users reported injuries.

For weeks, though, Peloton resisted recalling the machines, despite calls from regulators and politicians to do so. The Consumer Product Safety Commission, a watchdog group, had warned people not to use the Tread+ product in mid-April.

In a Friday filing with the Securities and Exchange Commission, Peloton said it is also being investigated by the SEC for its public disclosures related to those injuries. The company also said it has been named in several lawsuits associated with the recalls.

A spokesperson did not immediately respond to CNBC’s request for additional comment.

Peloton shares were down nearly 8 percent in premarket trading Friday, following a disappointing fiscal fourth-quarter financial report.

Peloton said it intends to cooperate with each of the investigations. “At this time, we are unable to predict the eventual scope, duration or outcome of the investigations,” the company added.

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