ectors A and B are given by: A = 24.15i + 22.01j B = 80.63i + 23.67j Find the scalar product AB.

8) A vector ä of magnitude 10.0 units and another vector b of magnitude 6.00 units differ in directions by 60.0°. Find (a) the scalar product of the two vectors and (b) the magnitude of the vector product āxb.

Using the definition of dot product: A B = ABCOS (0AB) = AxBx + Ay By + A₂B₂ Find the angle between the following vectors: (c) A = 1î + 3j+0k B = 3î + 1) + Ok A = 1î - 3j + 2k B = -31 + 1) + 0k (b) (d) A = 1î + 1ĵ + Ok B = 21-3j+0k A = 21-5j-1k B = 3î + 11 + 3k

Given two vector A = -5.00i –- 9.00j + 4.00k and B = -4.00i + 6.00j – 2.00k what is the vector product A × B.

6. Vector A has a magnitude of 5.00 units, and vector B has a magnitude of 9.00 units. The two vectors make an angle of 50.0° with cach other. Find A B. Note: In Problems 7 and 8, calculate numerical answers to three significant figures as usual. 7. Find the scalar product of the vectors in Figure P7.7. 118 32.8 N 132° 17.3 cm Figure P7.7 8. Using the definition of the scalar product, find the angles between (a) A = 3i-2j and B = 4i-4j. (b) A= -2i + 4j and B= 3i- 4j + 2k, and (c) A=i-2j + 2k and B = 3j + 4k. SECTION 7.4 Work Done by a Varying Force 9. A particle is subject to a force F that varies with position as shown in Figure P7.9. Find the work done by the force on the particle as it moves (a) from x = 0 to x = 5.00 m, (b) from x = 5.00 m to x = 10.0 m, and (c) from x= 10.0 m to x = 15.0 m. (d) What is the total work done by the force over the distance x= 0 tox= 15.0 m: 7, (N) X (m) 121 10 12 14 16 Figure P7.9 Problems 9 andl 22.

Vector A = 3 i + 3.8 j. Vector B = 5.1 i - 7.5 j. The dot product of the two is C = A ∙ B (i.e. A dot B). The value of C is:

1. The vector a has a magnitude of 5.00 units and the vector ba magnitude of 7.00 units. If the angle between the vectors is 53.00, find their scalar product or dot product.

Two vectors have the following magnitude, A = 8.9 m and B = 7 m. Their vector product is:  A⨯B = -1.8 m i + 13.8 m k. What is the angle (in degrees) between the vectors A and B?

A vector a of magnitude 17 units and another vector b of magnitude 8.5 units differ in directions by 72°. Find (a) the scalar product of the two vectors and (b) the magnitude of the vector product a×b.

Given the pair of vectors, A = (9.00î − 5.00ĵ ) and B =(−3.00î + 9.00ĵ ),use the definition of a scalar product to determine the following.   (a) the scalar product (b) the angle between the vectors (Enter an answer between 0 and 180 degrees.)                      ° (c) the angle ? between the vector A and the +x axis (Enter an answer between 0 and 180 degrees.)                      ° (d) the angle ? between the vector B and the +y axis (Enter an answer between 0 and 180 degrees.)                      °