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Explain the difference between a scalar and a vector with a detailed explanation.

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Let A= (3.0 m, 200south of east), B = (2.0 m, north), and C= (5.0 m, 700south of west). Draw and label A, B, and C with their tails at the origin. Use a coordinate system with the x-axis to the east. b. Write A, B, and C in component form, using unit vectors. c. Find the magnitude and the direction of D = A + B+ C.
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The diagram shows a vector A. P is the horizontal component of A, at an angle to A. d (c.) Which graph best shows the variation with of the magnitude of P? (a.) d Ꮎ 0 Á P 0 (rad) 0 (rad) O Graphs (a.) & (d.) only. O Graph (d.) only. O Graphs (a.) & (b.) only. O Graphs (a.), (b.) & (c.) only. O Graphs (a.) & (c.) only. O None of them. O Graph (c.) only. O Graph (b.) only. O Graph (a.) only. O All of them. EIN 2 16 N π 2 (b.) d (d.) d 0 (rad) 0 (rad) 16 IN π |-2
QUESTION 2 Which of the following is an accurate statement? O A. It is possible to add a scalar quantity to a vector. O B. Even though two vectors have unequal magnitudes, it is possible that their vector sum is zero. OC. Rotating a vector about an axis passing through the tip of the vector does not change the vector. OD. The magnitude of a vector is independent of the coordinate system used. O E. The magnitude of a vector can be zero even though one of its components is not zero.
if applicable gravity must equal 10 You are given three vectors. A = 5 m at 30 degrees B = 5 m at 150 degrees C = 5 m at 270 degrees Calculate the magnitude of the resultant vector R=A+B+C
Which of the following statements are true of scalars and vectors? List all that are TRUE. A vector quantity always has a direction associated with it. A scalar quantity can have a direction associated with it. Vectors can be added together; scalar quantities cannot. Vectors can be represented by an arrow on a scaled diagram; the length of the arrow represents the vector's magnitude and the direction it points represents the vector's direction.
1. Let v = -51 + 53 be a vector in R². (a) Find v. (b) Find the angle, 0, in degrees, that v makes with the positive x-axis. (Answer in radians between 0 and 27.) (c) Find a unit vector that points in the same direction as v. Answer in component form.
Explain why a vector cannot have a component greater than its own magnitude.
The Scalar Product The vectors A andB are given by A = 31 + 1j and B = -1î + 1j. (a) Determine the scalar product A - B. SOLUTION Conceptualize There is no physical system to imagine here. Rather, it is purely a mathematical exercise involving two (vectors Categorize Because we have a definition for the scalar product, we categorize this example as a substitution vy problem. Substitute the specific vector expressions for A and B: A-B = (31 + 1j) - (-1î + 1j) = [3i - (-1)i - [31 - 15 - 13 - (-1) + [1j - 15] The same result is obtained when we use the equation A -B = AB, + A8, + A,B, directly, where A, = 3, A, = 1, B, = -1 and 8, = 1. (b) Find the angle e between A and B. SOLUTION Evaluate the magnitudes of A and B using the Pythagorean theorem: A = VA,? + A, = B = V82 + B 2 = Use the equation A - B = AB cos(e) and the result from part (a) to find the angle (in degrees). cos(e) = AB EXERCISE As a particle moves from the origin to (7i + 5j) m, it is acted upon by a force given by (7î +…