A vector of magnitude 10 has its rectangular components as 8 and 6 along x and y axes. Find
the angles it make with these axes.
Answers
Explanation:
Given:
Magnitude of the vector=10 units
Rectangular components of the vector=8 along x axis and 6 along y axis
To find:
We have to find the angle made by the vector at x and y axis
Solution:
Let Angle made with x-axis = \alpha=α
Therefore
\ {Tan} \alpha= Tanα= =\frac{6}{8}=
8
6
=\frac{3}{4}=
4
3
\alpha=37^{\circ}α=37
∘
Let Angle made with y-axis =\beta
\tan \beta=tanβ= =\frac{8}{6}=
6
8
=\frac{4}{3}=
3
4
\beta=53^{\circ}β=53
∘
Answer:
Explanation:
Component along x-axis,
10cosα=8...............................(1)
Component along y-axis,
10sinα=6.................................(2)
Diving equation 2 by 1,
cosα
sinα
=
8
6
tanα=
4
3
α=tan
−
4
3
=36.869
0
Angle made with x-axis =36.869
0
Angle made with y-axis =90
0
−36.869
0
=53.13
0