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Q 26P

Physics For Scientists & Engineers
Found in: Page 73

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Short Answer

Given the vectors A=2.00i^+6.00j^ and B=3.00i^-2.00j^, (a) draw the vector sum C=A+B and the vector difference D=A-B. (b) Calculate C and D , in terms of unit vectors. (c) Calculate C and D in terms of polar coordinates, with angles measured with respect to the positive x axis.

a) The graph is drawn below.

b) C=5i^+4j^ and D=-1i^+8j^

c) |D|=8.06 and θD=97.1°

See the step by step solution

Step by Step Solution

Step 1: Define vector, polar coordinates, and unit vector

  • A quantity that has both magnitude and direction is called a vector. It's usually represented by an arrow with the same direction as the amount and a length proportionate to the magnitude of the quantity.
  • A vector does not have a position, even though it has magnitude and direction.
  • Polar coordinates are two integers that indicate the position of a point on a plane: a distance and an angle.
  • A unit vector is a vector with the same magnitude as the magnitude of the magnitude.

Step 2: (a) Plot the graph of the vector sum and vector difference

The vector sum C=A+B and the vector difference D=A-B.

Step 3: (b) Determine the vector total and difference

We just add or subtract the corresponding components to determine the vector total or difference.


Step 4: (c) Determine the polar coordinates

In order to find C and D in polar coordinates, we must first determine their magnitudes and angles with the +x-axis.


θD=tan-18-1=-82.9+180°=97.1°Hence, |D|=8.06 and θD=97.1°

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