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Let the vector v have an initial point at (0,5) and a terminal point at (-6, 1). Plot the vector v and afterwards follow the guided steps to analyze the vector. Click and drag to draw the directed line segment. ​

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Answer:

The magnitude of vector v is sqrt(52).

Explanation:

The vector v has an initial point at (0,5) and a terminal point at (-6, 1). To plot the vector, start at the initial point (0,5) and draw a line segment that ends at the terminal point (-6,1). This line segment represents the vector v.

To analyze the vector v, we can look at its components and magnitude. The components of a vector represent the change in x and y coordinates from the initial point to the terminal point. In this case, the x component is -6 - 0 = -6, and the y component is 1 - 5 = -4.

The magnitude of a vector represents its length or size. We can use the Pythagorean theorem to find the magnitude of vector v. The formula is: magnitude = sqrt(x^2 + y^2), where x and y are the components of the vector.

In this case, the magnitude of vector v is sqrt((-6)^2 + (-4)^2) = sqrt(36 + 16) = sqrt(52).

So the magnitude of vector v is sqrt(52).

By analyzing the components and magnitude of vector v, we can understand its direction and length. The x component of -6 means that the vector moves 6 units to the left, and the y component of -4 means that the vector moves 4 units downwards. The magnitude of sqrt(52) represents the overall length of the vector.

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