Vector A in polar coordinates, vector B in unit vectors: Find vector sum difference.

See attached file.

Vectors A in polar coordinates and vector B with unit vectors are given. Find a vector sum and a vector difference. Ignore units.

Vector A= 5 units at 53 degrees, and B= 5 i - 2 j in which i and j are unit vectors in x and y directions respectively.

PART a. Show A and B and vector sum C in a polygon (Not to scale) showing A + B = C.
SEE ATTACHMENT #1 for a diagram showing known data for A and B, and also a general triangle for showing law of cosines and law of sines.

PART b. Use the law of cosines to calculate the magnitude of C.

PART c. Express A with unit vectors, then find D with unit vectors, if D= B - A.

PART d. Using the answer to part c, construct a vector polygon (Not to scale) having D, B and A connected to show D= B - A.

PART a. Step 1.
Recall that vectors connected head-to-tail are added vectors, and their vector sum is the vector from the tail of the first to the head of the last vector. This arrangement is shown in ATTACHMENT #2. Notice that A and B are head to tail and C is from the tail of A to the head of ...

Solution Summary

The vector A in polar coordinates and vector B in unit vectors are determined. With a graph and good explanations, the problems are solved.

In the standard basis of P3 (i.e. {1,x,x^2}) p(x)=3-2x+5x^2, that is, it has coordinates p=(3,-2,5). Find the coordinates of this vector (polonomial) in the basis {1-x,1+x,x^2-1}

Hi, I am having a lot of difficulty understanding vectors, can you please assist me with these questions.
Given: position vector A = i hat.
position vector B = i hat + j hat + k hat.
1) Find A hat and B hat (unitvector in that direction).
2) Find position vector C in that plane perpendicular to position ve

The eastward component of vector A is equal to the westward component of vector B and their northward components are equal. Which one of the following statements is correct for these two vectors?
Choices:
Vector A is parallel to vector B
Vector A is anti-parallel to vector B
The magnitude of vector A is equal to the mag

So here is the question
Let A= {10, 30°} be a vector of magnitude 10 ( in some units) and pointing in a direction of 30°counter-clockwise from positive x.
Let B = { 7, 225°degree}
Find x and Y componens of these two vectors
A { AX= AY=
B { Bx= BY=
Find x and y components of the sum S= A+B
S= { Sx=
S

Please view the attached file for proper formatting on the following questions regarding polar coordinates.
1. Consider the polar coordinates:
x = rcos(theta)
y = rsin(theta)
Questions a) to e) can be seen in the attachment.

A particle moves along a parametrized curve given by
x(lamda)=cos(lamda), y(lamda)=sin(lamda), z(lamda)=lamda
Express the path of the curve in the spherical polar coordinates {r, theta, pheta}
where x = rsin(theta)cos(pheta)
y=rsin(theta)sin(pheta)
z=rcos(theta)
so that the metric is
ds^2=dr^2+(r^2)d(theta)^2+(r^2)sin

Two vectors lie in the xy-plane. Vector 1 has a magnitude of 3.00 m and makes an angle with the x-axis of 32.0 degrees when measured counterclockwise from the +x-direction. Vector 2 has a magnitude of 6.00 m and makes an angle of 145 degrees when measured counterclockwise from the +x-direction. Find the magnitude and angle with

1. Vector A = 119 grams @ 164°. What is Ax ?
2. Vector A = 119 grams @ 164°.What is Ay ?
3. Vector B = (114) xunitvector + (-32.8) yunitvector. Assume [grams] as the unit. What is the magnitude of B?
4. Vector B = (114) xunitvector + (-32.8) yunitvector. Assume [grams] as the unit. What is the direction of B in ra

1 Given a = 9i - 5j and b = 7i-4j, express i and j in terms of a and b
2 Given a=<4,5,-3> and b =<4,-2,2> determine whether a and b are parrallel, perpendicular, or neither.
3 Given F = 4i -2k;..... P(0,1,0) and Q(4,0,1) find the work W done by the force (F)moving a particle in a straight line from P to Q.
4 Given a