Question

Two vectors are given by; A ⃗=(2i ̂+3j ̂+4k ̂)units B ⃗=(4i ̂+6j ̂+8k ̂)units If it is known that ;

a.A ⃗+B ⃗+2C ⃗=0, Find C ⃗.

b. Find (A ⃗+2C ⃗).2B ⃗.

c.Find (A ⃗×B ⃗)

d.Find (A ⃗+B ⃗+2C ⃗)×(2A ⃗+B ⃗)

Answer #1

Two vectors are represented by F1 = -4i -5j and F2 = -2i +3j.
What is the angle between the two vectors?

Find the volume of the parallelepiped determined by the vectors
a, b, and c.
a = 2i + 4j − 4k, b = 3i − 3j +
3k, c = −4i + 4j + 3k
( ) cubic units

A) Find the angle between the vectors 8i-j + 4k and 4j + 2k
B) Find c so that the vectors 2i-3j + ck and 2i-j + 4k are perpendicular
C) Find the scalar projection and the vector projection of 2i +
4j-4 on 3i-3j + k

A) Find a vector that measures 3 in the direction of the vector
2i + 3j - k
B) Given the vectors a = 2i + 3j - k and b = -2i + 3j + k. Find
2a 3 b and |a-b|
C) Find the vector that goes from point P (2, -1,4) to point Q
(3, -2,6)

1) Find the angle θ between the vectors a=9i−j−4k and
b=2i+j−4k.
2) Find two vectors v1 and v2 whose sum is <-5,
2> where v1 is parallel to <-3 ,0> while v2 is
perpendicular to < -3,0>

Using MATLAB, create three vectors a = 4i, b = 2i - 4j, and c =
-2i + 3k, where i, j and k are unit vectors of three axes in
Cartesian coordinate system. Compute |?∙(?×?)| using the predefined
MATLAB commands and show that it is the volume of a parallelepiped
defined by three vectors a, b and c.

Vector A is referenced by (5i,-3j,10k) and vector B is
(2i,5j,8k)
determine the cross product vector C C=A*B
determine the magnitude of vector C
determine the directional angles: a,b,y
draw the vector C with represent to an x-y-z axis showing the
angles a,y,b

Homework #2
a) Find a vector perpendicular to the vectors 2i + 3j-k and 3i +
k
b)Find the area of the triangle whose vertices are (2, -1,1),
(3,2,1) and (0, -1,3)
c)Find the volume of the parallelepiped with adjacent axes PQ,
PR, and PS with P (1, -2.2), Q (1, -1.3), R (1,1,0), S (1,2,3 )

Consider the vectors |a>= (2i, 1-i, 4i) and |b>=(1-3i, 3i,
1-5i) Where I is the imaginary number
a) Normalize each vector |a> and |b>
b) Determine whether these two vectors are orthogonal or not

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...

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