Find the angles made by the vectors displaystyle{A}={5}{i}-{2}{j}+{3}{k} with the axes give a full correct answer

permaneceerc 2020-11-20 Answered
Find the angles made by the vectors A=5i2j+3k with the axes give a full correct answer
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

izboknil3
Answered 2020-11-21 Author has 99 answers
First note that the cosines of the angles a vector makes with the Cartesian coordinate axes are called the direction cosines.
Now let the given vector is
A=Axi^+Ayj^+Azk^
Let the vector A makes andgle α,βandγ with cordinate axes x, y and z, respectively.
Also, let l, m and n are the direction cosine along x-axis, y-axis and z-axis, respectively.
Then we have
l=cosα=Ax(Ax2+Ay2+Az2)12
m=cosβ=Ay(Ax2+Ay2+Az2)12
n=cosγ=Az(Ax2+Ay2+Az2)12
It is given that
Ax=5,Ay=2,Az=3
Thus we have
(Ax2+Ay2+Az2)12=52+(2)2+32=38
Thus angle with x-axis is
α=cos1(538)=35.78
The angle with y-axis is
β=cos1(138)=108.93
The angle with z-axis is
γ=cos1(338)=60.88
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-06-01
Find the vectors T, N, and B at the given point.
r(t)=<t2,23t3,t> and point <4,163,2>
asked 2021-05-14
Find a nonzero vector orthogonal to the plane through the points P, Q, and R. and area of the triangle PQR
Consider the points below
P(1,0,1) , Q(-2,1,4) , R(7,2,7)
a) Find a nonzero vector orthogonal to the plane through the points P,Q and R
b) Find the area of the triangle PQR
asked 2021-09-22

Find the volume of the parallelepiped with one vertex at the origin and adjacent vertices at (1,3,0),(2,0,2),and(1,3,1).

asked 2022-01-04
Determine whether the set equipped with the given operations is a vector space.
For those that are not vector spaces identify the vector space axioms that fail.
The set of all pairs of real numbers of the form (x,0) with the standard operations on R2.
V is a vector space.
V is not a vector space, and Axiom 7,8, 9 fails to hold.
V is not a vector space, and Axioms 4 and 5 fail to hold.
V is not a vector space, and Axioms 2 and 3 fail to hold.
V is not a vector space, and Axiom 10 fails to hold.
asked 2022-03-20

Determine the average value of F(x, y, z) = xyz throughout the cubical region D
bounded by the coordinate planes and the planes x = 2, y − 2, z = 2 in the first octant.

asked 2021-12-02
Find direction numbers for the line of intersection of the planes x+y+z=1 and x+z=0
asked 2021-09-16
The curvature given by the vector function r is
k(t)=|r(t)×r(t)||r(t)|3
Use the formula to find the curvature of r(t)=15t, et, et at the point (0, 1, 1)