Question 1173575: Find the component form of v given its magnitude and the angle it makes with the positive x-axis. Sketch v.
Magnitude Angle
v= 2 v in the direction 3i + 4j
v=
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! Let's break down this problem step-by-step.
**1. Find the Unit Vector in the Direction of 3i + 4j**
* The vector 3i + 4j has components <3, 4>.
* Find the magnitude of this vector: ||3i + 4j|| = √(3² + 4²) = √(9 + 16) = √25 = 5.
* The unit vector in the direction of 3i + 4j is: (3i + 4j) / 5 = <3/5, 4/5>.
**2. Find the Component Form of v**
* The magnitude of v is 2.
* The direction of v is the same as the unit vector we just found: <3/5, 4/5>.
* Multiply the magnitude of v by the unit vector to find the component form of v:
* v = 2 * <3/5, 4/5> = <6/5, 8/5> = <1.2, 1.6>.
**3. Sketch v**
* Draw the x-y coordinate plane.
* Start at the origin (0, 0).
* Move 1.2 units along the positive x-axis.
* Move 1.6 units along the positive y-axis.
* Draw an arrow from the origin to the point (1.2, 1.6). This arrow represents the vector v.
**Component Form of v:**
v = <1.2, 1.6>
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