Addition of cartesian vectors

1. Addition of Cartesian Vectors

2. 1-The shaft S exerts three force components on the die D. Find the magnitude
and coordinate direction angles of the resultant force. Force 𝐹2
acts within the octant shown.
Magnitude of 𝐹𝑅 = ?
Direction angles of 𝐹𝑅 =?
(𝐜𝐨𝐬 ⍺) 𝟐+(𝐜𝐨𝐬 𝜷) 𝟐+(𝐜𝐨𝐬 𝜸) 𝟐=1

3. 2-Three forces act on the ring. If the resultant force 𝑭 𝑹 has a magnitude and
direction as shown, determine the magnitude and the coordinate direction angles of
force 𝑭 𝟑.
Magnitude of 𝐹3 = ?
Direction angles of 𝐹3 =?

4. 𝐴 𝑥=Asin ø cos θ
𝐴 𝑦=Asin ø sin θ
𝐴 𝑧=Acos ø
A=Asin ø cos θi+Asin ø sin θj+Acos øk

5. 3-If the resultant force acting on the bracket is directed along the positive y axis, determine
the magnitude of the resultant force and the coordinate direction angles of F so
that 𝛽 > 90°.
𝛽 <90 Magnitude of 𝐹 = ?
If
𝑭 𝑹 directed along the positive y axis Direction angles of 𝐹 =?

6. • 𝐴 𝑥=Asin ø cos 𝜃
• 𝐴 𝑦=Asin ø sin 𝜃
• 𝐴 𝑧=Acos ø
• (cos ⍺)2
+(cos 𝛽)2
+(cos 𝛾)2
=1

7. 4-Determine the magnitude and coordinate
direction angles of 𝑭 𝟐 so that the resultant of the two forces
acts along the positive x axis and has a magnitude of 500 N.
Magnitude of 𝐹2 = ?
if 𝑭 𝑹=500 i
Direction angles of 𝐹2 =?

8. 5- If the resultant force acting on the bracket is to be 𝐹𝑅 = {800j} N
, determine the magnitude and coordinate direction angles of F.
Magnitude of 𝐹 = ?
if 𝑭 𝑹=800 j
Direction angles of 𝐹 =?