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Physics
Physics
Problem
A particle in equilibrium is subjected to four forces
F
⃗
1
=
−
10
k
^
,
F
⃗
2
=
u
(
4
13
i
^
−
12
13
j
^
+
3
13
k
^
)
\vec{F}_1 = -10\hat{k}, \quad \vec{F}_2 = u\left(\frac{4}{13}\hat{i} - \frac{12}{13}\hat{j} + \frac{3}{13}\hat{k}\right)
F
1
=
−
10
k
^
,
F
2
=
u
(
13
4
i
^
−
13
12
j
^
+
13
3
k
^
)
F
⃗
3
=
v
(
−
4
13
i
^
−
12
13
j
^
+
3
13
k
^
)
\vec{F}_3 = v\left(-\frac{4}{13}\hat{i} - \frac{12}{13}\hat{j} + \frac{3}{13}\hat{k}\right)
F
3
=
v
(
−
13
4
i
^
−
13
12
j
^
+
13
3
k
^
)
and
F
⃗
4
=
w
(
cos
θ
i
^
+
sin
θ
j
^
)
\vec{F}_4 = w(\cos\theta\hat{i} + \sin\theta\hat{j})
F
4
=
w
(
cos
θ
i
^
+
sin
θ
j
^
)
Find the values of
u
,
v
u, v
u
,
v
and
w
w
w
in terms of
θ
\theta
θ
.
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