Answer :
Answer:
a) [tex]a_{x} =3[/tex] b) [tex]a_{y} =0[/tex]
c) [tex]b_{x} =3.46[/tex] d) [tex]b_{y} =2[/tex]
e) [tex]c_{x} =0[/tex] f) [tex]c_{y} =10[/tex]
g) p = -5.77 h) q=5
Explanation:
Diagram for given question is attached below in fig 1
Part (a) (b)
for vector [tex]\vec{a}[/tex]
θ = 0°
[tex]a_{x} = 3 cos (0)\\a_{x} = 3\\a_{y} = 3 sin (0)\\a_{y} = 0[/tex]
Part (c) (d)
for vector [tex]\vec{b}[/tex]
θ = 30°
[tex]b_{x} = 4 cos (30)\\b_{x} = 3.46\\b_{y} = 4 sin (30)\\b_{y} = 2[/tex]
Part (e) (f)
for vector [tex]\vec{c}[/tex]
θ = 90°
[tex]c_{x} = 10 cos (90)\\c_{x} = 0\\c_{y} = 10 sin (90)\\c_{y} = 10[/tex]
Part (g) (h)
[tex]\vec{c} = p\vec{a} + q\vec{b}[/tex]
[tex]c =c_{x} \hat{i} + c_{y}\hat{j}\\as a_{y} =0\\c_{x} \hat{i} + c_{y}\hat{j} = pa_{x} \hat{i} +q(b_{x} \hat{i} +b_{y} \hat{j} )\\c_{x} \hat{i} = pa_{x} \hat{i} +qb_{x} \hat{i}\\c_{y}\hat{j} =qb_{y}\hat{j}[/tex]
[tex]q=\frac{c_{y}}{b_{y}} \\q=\frac{10}{2}\\q=5[/tex]
[tex]c_{x} \hat{i} = pa_{x} \hat{i} +qb_{x} \hat{i}\\0 = p(3) + (5)(3.46)\\p = -5.77[/tex]
Three vectors in Fig 3.33 have magnitude and angle (direction) has the value of component as,
- (a) The x component of vector a is 3 m.
- (b) The y component of vector a is 0 m.
- (c) The x component of vector b is 3.46 m.
- (d) The y component of vector b is 2 m.
- (e) The x component of vector c is 0.
- (if) The y component of of vector c is 10 m.
- (g) The value of p is -577 m.
- (h) The value of q is 5 m.
What is vector components?
A vector components is the quantity which has both the magnitude and the direction.
Given infroamtion-
The image of the three vectors is attached below.
(a) the x component vector a and-
The x component from the figure can be given as,
aₓ=(a)cos(0)=a
aₓ=3 m
Thus x component vector a is 3 meters.
- (b) The y component of a-
The y component from the figure can be given as,
[tex]a_y[/tex]=(a)sin(0)=0
[tex]a_y[/tex]=0
Thus y component vector a is 0 meters.
- (c) The x component vector b
The x component of vector b from the figure can be given as,
bₓ=b*cos(30)=4*cos(30)
bₓ=3.46 m
Thus x component vector b is 3.46 meters.
- (d) the y component of vector b-The y component of vector b from the figure can be given as,
b(y)=b*sin(30)=4*sin(30)
b(y)=2 m
Thus y component vector b is 2 meters.
- (e) the x component of vector c-
The x component of vector c from the figure can be given as,
cₓ=(c)*cos(90)=10*cos(30)
cₓ=0 m
Thus x component vector c is 0 meters.
- (if) the y component of vector c-
The y component from the figure can be given as,
[tex]c_y[/tex]=(c)*sin(90)=10*1
[tex]c_y[/tex]=10
Thus y component vector c is 10 meters.
- g), h) Value of p and q-
[tex]\vec c=p\vec a +q\vec b[\tex]
[tex]c_x\hat i+c_y\hat j=p(a_x\hat i+b_y\hat j)+q(b_x\hat i+b_y\hat j)[\tex]
Put the values we get two equation as,
-5=3*p+3.46*q
8.66=2*q
Solving these equation we get,
p=-6.67
q=4.33
Hence,
- (a) The x component of vector a is 3 m.
- (b) The y component of vector a is 0 m.
- (c) The x component of vector b is 3.46 m.
- (d) The y component of vector b is 2 m.
- (e) The x component of vector c is 0.
- (if) The y component of of vector c is 10 m.
- (g) The value of p is -577 m.
- (h) The value of q is 5 m.
Learn more about the vector components here;
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