"Vector A⃗ , which is shown in the figure, has a magnitude of 10 and a direction angle of 60º. What is the magnitude and directi

Question

goldfiish [28.3K]

3 years ago

15

"Vector A⃗ , which is shown in the figure, has a magnitude of 10 and a direction angle of 60º. What is the magnitude and directi

on angle (as measured counterclockwise from the positive x-axis) of −A⃗ /2?
-5, 60º
5, 240º
5, -30º
-5, -30º
-5, 240º"

Mathematics

2 answers:

lyudmila [28] · Answer 1 · 2022-05-16T12:13:02+03:00

Answer: Second option 5, 240°

Magnitude of vector A=10
Direction angle of vector A=60°

-A/2 is a vector with magnitude equal to the half of the magnitude of the vector A and direction opposite to the direction of vector A, because the minus sign, then:

Magnitude of vector -A/2=Magnitude of vector A / 2 =10/2→
Magnitude of vector -A/2=5

Direction angle of vector -A/2=Direction angle of vector A + 180°=60°+180°→
Direction angle of vector -A/2=240°

Answer: Second option 5, 240°

vovikov84 [41] · Answer 2 · 2022-05-16T14:24:59+03:00

The magnitude and direction angles ( as measured counterclockwise from the positive x - axis ) of - A / 2 is 5 and 240º

<h3>Further explanation</h3>

Vector is quantity that has magnitude and direction.

One example of a vector is acceleration.

Let us now tackle the problem !

This problem is about Vector Diagram.

<u>Given:</u>

Vector A = (10 cos 60°) i + (10 sin 60°) j = 5 i + 5√3 j

<u>Unknown:</u>

Vector A/2 = ?

<u>Solution:</u>

$\overrightarrow{A} = 5~\widehat{i} + 5\sqrt{3}~\widehat{j}$

$-\overrightarrow{A} / 2 = -(5~\widehat{i} + 5\sqrt{3}~\widehat{j}) \div 2$

$-\overrightarrow{A} / 2 = -\frac{5}{2} ~\widehat{i} - \frac{5}{2}\sqrt{3}~\widehat{j}$

$|-\overrightarrow{A} / 2| = \sqrt{(-\frac{5}{2})^2 + (- \frac{5}{2}\sqrt{3})^2}$

$|-\overrightarrow{A} / 2| = \sqrt{25}$

$|-\overrightarrow{A} / 2| = 5$

$\tan \theta = (- \frac{5}{2}\sqrt{3}) \div (-\frac{5}{2})$

$\tan \theta = \sqrt{3}$

$\theta = 180^o + 60^o$

$\theta = 240^o$

From the results above, it can be concluded that the magnitude and direction angles ( as measured counterclockwise from the positive x - axis ) of - A / 2 is 5 and 240º

<h3>Learn more</h3>