Vector resolution and addition

Vector resolution and addition
Zeenath Asks:

Sir please send me the answers with the reasons and steps

  1. the drawing on the left shows two vectors A and B, and the drawing on the right shows their components.

    The scalar components of these vectors are:

    When the vectors A and B are added, the resultant vector is R, so that RAB. What are the x– and y-components of R?
  2. the displacement vectors A and B, when added together, give the resultant vector R, so that RAB. Use the data in the drawing to find the magnitude R of the resultant vector and the angle q that it makes with the +x axis.

 

 

Answer

In the first question as you can see that the X components (Ax and Bx being equal and opposite will cancel each other and therefore the X com ponent of the resultant is zero.

The Y components will add up and therefore the Y component of resultant = 3.4+3.4 = 6.8 m and this itself is the magnitude of the resultant as the X components have canceled out.

Hnit for Answer to the second question

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Comments

  1. R^2=A^2+B^2+2ABcosθ
    θ is the angle between the vectors
    For the second question use θ = 90+23 =113

    1. The vectors are given in blue colour, if you extend them, the angle between their directions can be found to be 90+23 =113

      1. Sir, Can u explain it with the help of a figure? So that i can understand the concept more clearly.

  2. Also the answer is to be found out using resolving, we dont have the formula used by Mr. sivaraman (in syllabus).

  3. Sir,
    please help me to solve the following problems:

    1) let A and B be the two vectors of magnitude 10 unit each. If they are inclined to the X-axis at angles 30 degree and 60 degree respectively, find the resultant.

    2) A force F=(5i + 3j + 2k)N acting on a body first displaces it by 2m along the x axis and then by 3m along the y axis. What is the total work done by the force?