The magnitude and direction angles ( as measured counterclockwise from the positive x - axis ) of - A / 2 is 5 and 240º
Further explanation
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.
Given:
Vector A = (10 cos 60°) i + (10 sin 60°) j = 5 i + 5√3 j
Unknown:
Vector A/2 = ?
Solution:
\(\overrightarrow{A} = 5~\widehat{i} + 5\sqrt{3}~\widehat{j}\)
\(-\overrightarrow{A} / 2 = -(5~\widehat{i} + 5\sqrt{3}~\widehat{j}) \div 2\)
\(-\overrightarrow{A} / 2 = -\frac{5}{2} ~\widehat{i} - \frac{5}{2}\sqrt{3}~\widehat{j}\)
\(|-\overrightarrow{A} / 2| = \sqrt{(-\frac{5}{2})^2 + (- \frac{5}{2}\sqrt{3})^2}\)
\(|-\overrightarrow{A} / 2| = \sqrt{25}\)
\(|-\overrightarrow{A} / 2| = 5\)
\(\tan \theta = (- \frac{5}{2}\sqrt{3}) \div (-\frac{5}{2})\)
\(\tan \theta = \sqrt{3}\)
\(\theta = 180^o + 60^o\)
\(\theta = 240^o\)
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
Learn more
- Velocity of Runner : https://brainly.com/question/3813437
- Kinetic Energy : https://brainly.com/question/692781
- Acceleration : https://brainly.com/question/2283922
- The Speed of Car : https://brainly.com/question/568302
Answer details
Grade: High School
Subject: Mathematics
Chapter: Vectors
Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle , Speed , Time , Rate, Stream , Vector
