Use the definition of scalar product, a 6.0î + 6.0ĵ two vectors given by a Number IN = b = ab cos 0, and the fact that a · b = axbx + ayby + a₂b₂ to calculate the angle between the 2.0î + 2.0ĵ + 3.0k. → + 6.0k and b = Units

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

Q(2) Consider the two vectors A= 31 – 2j and B = 2i – 3j. Calculate the angle between the two vectors A) 146° B) 47.7° C) 70° D) 22.6° O 1. D O 2. B O 3. C O 4. A

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.

Calculate the angle between the vectors A=(5;4) and B=(2;8)

"What is the angle between two vectors A and B given that Ax =3, Ay = -2, Bx =2, and By =3?"

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?

3. Calculate the scalar product of vectors A and B. Illustrate with complete and correct labels (rough estimation only). Ā = 125 units, -120° and B= 187 units, 25.0° south of east.

Two position vectors are given by Á = (4.00m)î – (2.00m)j – (3.00m)k and B= (4.00m)i - (5.00m)k. What is the scalar product of (3Á) · B? O (16.0m²)î + (15.0m²)k O 31 m2 (48.0m2)i + (45.0m2)k O 93 m2 O None of the above.