Finding Magnitude and Direction using Component Method?

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To find the magnitude and direction of vector D = A + B + C, first calculate the components by summing the respective i and j components of vectors A, B, and C. For vector A, the magnitude can be determined using the formula |A| = √((-2)² + 3²), and the angle with the +x axis can be found using θ = arctan(3/-2). Similarly, for vector E = -A - B + C, the components must be calculated, and its magnitude and direction can be derived using the same methods. The discussion emphasizes the importance of understanding vector addition and the component method for solving these types of problems. Mastering these calculations is crucial for accurately determining vector magnitudes and directions.
OUmecheng
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Homework Statement

Consider the three displacement vectors A = ( -2i + 3j ) m, B = ( 2i + 7j ) m, and C = ( -7i + 5j ) m. Use the component method to determine the following.

(a) The magnitude and direction of D = A + B + C
|D| = ___ m
θ = ___° (from the +x axis)

(b) The magnitude and direction of E = -A - B + C

|D| = ___ m

θ = __° (from the +x axis)

The Attempt at a Solution

I don't even know where to begin.
 
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OUmecheng said:

Homework Statement



Consider the three displacement vectors A = ( -2i + 3j ) m, B = ( 2i + 7j ) m, and C = ( -7i + 5j ) m. Use the component method to determine the following.

(a) The magnitude and direction of D = A + B + C
|D| = ___ m
θ = ___° (from the +x axis)

(b) The magnitude and direction of E = -A - B + C

|D| = ___ m

θ = __° (from the +x axis)

The Attempt at a Solution



I don't even know where to begin.

Can you find the components of vector D?


For vector A:

Can you calculate |A|, the magnitude of A?

Can you calculate the angle which vector A make with the +x-axis?
 

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