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Question Video: Finding the Polar Form of a Vector Mathematics

Complete the following: If π = β©2, 10Β°βͺ, then the polar form of vector 8π is οΌΏ.

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Video Transcript

Complete the following. If vector π has magnitude two and angle 10 degrees, then the polar form of vector eight π is what.

Remember, a vector is a way of describing the magnitude, or size, and direction of a path, denoted by a line segment. When we describe a vector using polar form, we use the magnitude, π, which essentially means the length of the path from the start point to endpoint, and an angle π. In particular, this is the angle that the line segment makes with the positive π₯-axis in a counterclockwise direction. This means that the vector π has a length of two units and makes an angle of 10 degrees with the positive π₯-axis in a counterclockwise direction. We can represent this on the Cartesian plane by assuming it starts at the origin as shown.

So, with this in mind, letβs represent the vector eight π in polar form. Remember, when we multiply a vector by a scalar, this changes the length of the line segment. We can represent this diagrammatically as shown. For the vector eight π, the line segment is eight times the length of vector π. The direction remains unchanged. In fact, we can say that the angle that the vector eight π makes with the positive real axis is 10 degrees, as in the case of the original vector. This means we can write the vector eight π in polar form by simply multiplying the magnitude of vector π by eight and leaving the angle unchanged. Hence, the polar form of the vector eight π is 16, 10 degrees.

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