Thank you for visiting A vector has an x component of 24 0 units and a y component of 36 6 units Find the magnitude and direction of this. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
The vector has a magnitude of approximately 43.8 units and a direction of 122.9°.
We can find the magnitude and direction of the vector using the Pythagorean theorem and trigonometry.
The magnitude (or length) of the vector can be found using the formula:
magnitude = √(x²+y²)
here x is x component of the vector and y is y component of the vector.
Reserving given values:-
magnitude = √[(-24.0)² + (36.6)²]
magnitude = √(576 + 1339.56)
magnitude = √1915.56
magnitude = 43.8
Therefore, the magnitude of the vector is approximately 43.8 units.
The direction of the vector can be found using the inverse tangent function, which is defined as:
∠ = tan⻹(y/x)
Reserving given values:-
∠ = tan⻹(36.6/-24.0)
∠ = -57.1 degrees
Since the x component of the vector is negative and the y component of the vector is positive, the vector is in the second quadrant of the Cartesian plane. Therefore, the direction of the vector is 180 degrees minus the calculated angle, or:
direction = 180 - 57.1
direction = 122.9 degrees
Therefore, the vector has a magnitude of approximately 43.8 units and a direction of 122.9 degrees.
To know more about magnitude please refer: https://brainly.com/question/9774180
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