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 .
Suppose given that Vector is R and it makes angle with +x-axis, then it's components are given by:
Rx = Horizontal component = R*cos
Ry = Vertical component = R*sin
Using above rule:
Vector A = 2.80 cm, 60.0 deg above +x axis (In 1st quadrant both x and y ar epositive)
Ax = A*cos = 2.80*cos 60 deg = 1.40 cm
Ay = A*sin = 2.80*sin 60 deg = 2.425 cm
Vector B = 1.90 cm, 60.0 deg below +x axis (In 4th quadrant x is +ve and y is negative)
Bx = B*cos = 1.90*cos 60 deg = 0.95 cm
By = -B*sin = -1.90*sin 60 deg = -1.645 cm
Now we need to find,
C = B - A = B + (-A)
A = Ax i + Ay j
(-A) = -Ax i - Ay j = -1.40 i - 2.425 j
B = Bx i + By j = 0.95 i - 1.645 j
So,
C = (Bx - Ax) i + (By - Ay) j
C = (0.95 - 1.40) i + (-1.645 - 2.425) j
C = -0.45 i - 4.07 j
Magnitude of vector C will be:
|C| = |B - A|
|C| = sqrt ((-0.45)^2 + (-4.07)^2)
|C| = 4.0948 cm = 4.10 cm
Direction of vector C will be:
Direction = 180 + arctan (|Cy|/|Cx|)
Direction = 180 + arctan (4.07/0.45) = 180 + 83.7
Direction = 263.7 CCW from +ve x-axis
Part C.
Please Upvote.
Let me know if you've any query.
Vector A⃗ is 2.80 cm long and is 60.0∘ above the x-axis in the first quadrant....
Vector A is 2.80 cm long and is 60.0° above the x-axis in the first quadrant. Vector B is 1.90 cm long and is 60.0° below the x-axis in the fourth quadrant (the figure (Figure 1)). Part G You may want to review (Page) Use components to find the magnitude of B-A For related problemsolving tips and strategies, you may want to view a Video Tutor Solution of Using components to add vectors. IO ALDA O ? Submit Request Answer...
A⃗ = 10.0 @ 30°above the +x-axis; B⃗ = 12.0 @ 60°above the +x-axis; and C⃗ = 15.0 @ 50°below the +x-axis. What is the magnitude of A⃗ +B⃗ +C⃗ ?
Vector a is 3m long and is 60° above x-axis in the first quadrant. Vector b is 5m long and is 50° below the x-axis in the fourth quadrant. Find aa + b, ba-b, c) b-a. Provide answers to a)-c) in both, unit-vector notations and in terms of magnitude and direction.
Vector A⃗ has components Ax = 1.24 cm , Ay = 2.36 cm ; vector B⃗ has components Bx = 4.03 cm , By = -3.74 cm . Find the components of the vector sum A⃗ +B⃗ Find the magnitude of the vector sum A⃗ +B⃗ Find the counterclockwise angle the vector sum A⃗ +B⃗ makes with the +x axis, in interval [0,360]∘. Find the components of the vector difference B⃗ −A⃗ . Find the magnitude of the vector difference...
Vector ä is 3m long and is 60° above x-axis in the first quadrant. Vector b is 5m long and is 50° below the x-axis in the fourth quadrant. Find ajä + b, ba-b, c) b-a. Provide answers to a)-c) in both, unit-vector notations and in terms of magnitude and direction For two vectors mentioned in the problem 3, find ab and axb (in terms of magnitude and direction). 3. 4.
Vector A⃗ has components Ax = 1.28 cm , Ay = 2.23 cm ; vector B⃗ has components Bx = 4.27 cm , By = -3.77 cm . Find the components of the vector sum A⃗ +B⃗ . Find the magnitude of the vector sum A⃗ +B⃗ . Find the counterclockwise angle the vector sum A⃗ +B⃗ makes with the +x axis. Please give your answer in the interval [0,360]∘. Find the components of the vector difference B⃗ −A⃗ . Find the magnitude...
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 components Ax= 1.80 cm , Ay= 2.25 cm ; vector B⃗ has components Bx= 4.10 cm , By= -3.50 cm . Find the x-component of the vector sum A⃗ +B⃗ . Find the y-component of the vector sum A⃗ +B⃗ . Find the magnitude of A⃗ +B⃗ .
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
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 B⃗ −A⃗ B⃗ −A⃗ . please show calculation