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Addition of Cartesian Vectors
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
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 =?
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
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 =?
• 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
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 =?
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 =?
Addition of cartesian vectors

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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 =?