Let A⃗ = (3.0 m, 20 ∘ south of east), B⃗ = (2.0 m, north), C⃗ = (5.0 m, 70 ∘ south of west).
Use a coordinate system with the x-axis to the east. Find the direction of D⃗ =A⃗ +B⃗ +C⃗ .
Concept - Express each vector along coordinate axes in component form and use vector addition method to find the required direction as shown below
***********************************************************************************************
This concludes the answers. If there is any mistake or
omission, let me know immediately and I will fix
it....
Calculate (A⃗ ×B⃗ )⋅C⃗ for the three vectors A⃗ with magnitude A = 4.98 and angle θA = 27.1 ∘ measured in the sense from the +x - axis toward the +y - axis, B⃗ with B = 4.06 and θB = 60.6 ∘, and C⃗ with magnitude C = 6.00 and in the +z - direction. Vectors A⃗ and B⃗ are in the xy-plane.
Vector A⃗ is 2.80 cm long and is 60.0∘ above the x-axis in the first quadrant. Vector B⃗ is 1.90 cm long and is 60.0∘ below the x-axis in the fourth quadrant (the figure (Figure 1) Use components to find the magnitude of B⃗ −A⃗ Use components to find the direction of B⃗ −A⃗ . Sketch the vector subtraction C⃗ =B⃗ −A⃗ .
Let C⃗ = (2.15 m, 15 ∘ above the negative x-axis) and D⃗ = (39.6 m, 30 ∘ to the right of the negative y-axis). Find the x-component and the y-component of C⃗ . Find the x-component and the y-component D⃗ .
A bug travels directly north for 4.0 m, followed by 2.0 m at 30o South of East, and finally 3.0 m directly west. Sketch these three vector displacements. Break each vector into their components and find the total displacement. Bonus: What is the magnitude and direction of the total displacement?
Let C⃗ = (3.75 m, 15 ∘ above the negative x-axis) and D⃗ = (39.6 m, 30 ∘ to the right of the negative y-axis). A) Find the x-component and the y-component of C⃗ . Enter your answers numerically separated by a comma. B) Find the x-component and the y-component of C⃗ . Enter your answers numerically separated by a comma.
Vector A⃗ has components Ax= 1.80 cm , Ay= 2.25 cm ; vector B⃗ has components Bx= 4.10 cm , By= -3.50 cm . Find the direction of A⃗ +B⃗ . (Let the direction be the angle that the vector makes with the +x-axis, measured counterclockwise from that axis.) please show calculations
Vector A⃗ has a magnitude of 29 m and makes an angle of 30∘ above the positive x axis. Vector B⃗ has a magnitude of 10 m and is oriented 60∘ to the left of the y axis. Find the magnitude and direction of: a) A⃗ − B⃗ b) 2A⃗ + B⃗ c) −A⃗ + 3B⃗
A⃗ =( 26 m )x^+( -11 m )y^. B⃗ =( 3.5 m )x^+( 16 m )y^. Find the direction of vector A + B
you walk east (+X direction) for 3.0 km, then north for 6.0 km, then west for 5.0 km and then stop. In what direction and what distance should you walk to follow a straight line from where you stopped back to where you started? Refrence the direction relative tp the east.
A runner is training for an upcoming marathon by running around a 112-m-diameter circular track at constant speed. Let a coordinate system have its origin at the center of the circle with the x-axis pointing east and the y-axis north. The runner starts at (x, y) = (56 m, 0 m) and runs 2.5 times around the track in a clockwise direction. What is the magnitude of his displacement vector? ............. Whar is the direction of his displacement vector? West...