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

Comments

  1. Sivaraman says:

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

  2. Zeen says:

    θ is the angle between the vectors. ie; between A and B. Why you took this 90+23???

    1. admin says:

      Angle must be taken between the directions of the vectors.

    2. admin says:

      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. Zeen says:

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

  3. Zeen says:

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

    1. Zeen says:

      Thanks alot sir

  4. AVIK DAS says:

    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?