Q:1 a)Take any two vectors A and B in three dimensional Cartesian coordinate system of your choice and prove the following statements: Dot product of vectors A and B is a scalar quantity Cross product of vectors A and B is a vector quantity Note: Choose same vectors for both statements. b) A ball is kicked at an angle of 35° with the ground. What should be the initial velocity of the ball so that it hits a target that is 30 meters away at a height of 1.8 meter? What is the time for the ball to reach the target?

Vector ?⃗has a magnitude of 75.0cm and points at 30° above the positive x-axis. Vector?⃗⃗has a magnitude of 95.0 cm and points along the negative x-axis. Determine the x and y components of the sum of these two vectors Determine the magnitude and direction of the sum of these two vectors. Determine the dot product of vectors ?⃗and ?⃗⃗(?⃗∙?⃗⃗).  Determine the magnitude of the cross product (|?⃗×?⃗⃗|).

What is the direction of the vector product A × B? Use the legend in the box to indicate direction. a В (out) (out) O (in) zero in C b zero a e h out

How would I figure out the adding and subtracting parallel vectors? how would I figure out the adding and subtracting anti-parallel vectors?

Determine the x and y components of the following three vectors in the xy plane. (a) A 6-m displacement vector that makes an angle of 34° clockwise from the +y direction. x:   m y:   m (b) A 29-m/s velocity vector that makes an angle of 39° counterclockwise from the -x direction. x:   m/s y:   m/s

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.

Bruce begins 7 kilometers to the north of town and rides his bike along a straight trail which leads to a park 3km west of town. It takes him 20 minutes to cover this distance. Write a vector in component form that describes his ride while also finding the magnitude and direction of this vector. Also, find the component of Bruce's motion which is in the direction of SW using a unit vector that uses both forms of the dot product (algebraic and geometric), then write parametric equations expressing his motion with the town being represented by the origin and t=0 being his starting point. Using these equations, what is his position after 5 minutes? Then eliminate the parameter to get a rectangular equation for this linear path and verify algabraically amd graphically that this equation represents the line.

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

4) Two vectors have equal magnitudes of 2.0 m. Find graphically the angle between them if the magnitude of their resultant is (a) 3.0 m; (b) 1.0 m. In each case use the law of cosines to confirm your answer. Problems 3 and 4 are graphical solutions. Please use a protractor, ruler, and compass and work as accurately as possible. Alternatively, you could use a vector drawing program to work out the geometry

12.0 B = 5.0 F = 20.0 86400 365) %3D 24 (6)60) = Esc 60° A = 10.0 30 30° 53° D = 20.0 37° Assuming the +x-axis is horizontal to the right for the vectors in the figure, find the following scalar products. a. Ā . B- b. Č - (- 3) - c. Dx F- a. (5 x F) - ( x Ã) -