Question

Two vectors given below, A and B, are located in a standard 3-D cartesian coordinate system: A = 5i + 2j - 4k B = 2i + 5j + 5k a. Find the magnitude of the sum of A and B. b. Find the dot product of A and B. What does this result tell you about A and B? c. Find a vector C, with non-zero magnitude, that is perpendicular to both A and B.

Answer #1

Two 3D vectors, A and B , are represented in terms of the
Cartesian basis unit vectors, i , j , k as follows:
A=2i-3j+k
B=10i+9j-4k
1) plot A and B in a Cartesian coordinate system
2) calculate A + B
3) calculate A · B using the scalar product formula
4) calculate the magnitudes of A and B
5) calculate the angle between A and B
6) calculate A x B using the determinant formula
7) show that the...

2. Calculate, from vectors A, B, C and D, the following:
• The projection of vector A on vector B
• The area of the parallelogram that has the A and B vectors
• The magnitude of the resulting vector of the AXB product
• The CXD product and the direction of the resulting vector
• Calculate the angle between vectors C and D
• Calculate the magnitude (C · D) C
• Find CXD · D
A = -3i...

Consider two vectors ?⃗⃗ :( 30.0 m, 20.0degrees North of East)
and ?⃗⃗ : (50.0 m, 30.0degrees West of North).
a- Represent both vectors in an x-y coordinate system and find the
components of vector ?⃗⃗ and ?⃗⃗⃗ .
b- Express vector ?⃗⃗ = ?? ⃗⃗⃗ - ?/3 ?⃗⃗⃗ as a linear combination
of the unit vectors.
c- Calculate the magnitude and direction of vector ?⃗⃗

Your task will be to derive the equations describing the
velocity and acceleration in a polar coordinate
system and a rotating polar vector basis for an object in general
2D motion starting from a general
position vector. Then use these expressions to simplify to the case
of non-uniform circular motion, and
finally uniform circular motion.
Here's the time-dependent position vector in a Cartesian coordinate
system with a Cartesian vector
basis: ⃗r(t)=x (t)
̂
i+y(t)
̂
j where x(t) and y(t)...

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