Question

find the resultant of two vector when two vectors along
1. same plane
2. at right angle at each other

Answer 1

Answer:

when they are in the same plane then add the both magnitude and when they are perpendicular then subtract their magnitude

Answer 2

Answer:

1. Same plane can be in 2 ways:

 a. Same direction  - (i am considering this one )

 b. Opposite direction

Explanation:

1. a. Same direction

R = $\sqrt{p^{2} + q^{2} + 2pq cos}$ theta

R = $\sqrt{p^{2} + q^{2} + 2pq cos0}$

R = $\sqrt{p^{2} + q^{2} + 2pq}$    ----------------------------[Cos 0 = 1]

  = $\sqrt{(p + q)^{2} }$

R = p + q

Using:  Tan ∝ q sin theta / p cos theta

• Tan ∝ = q sin 0 / p cos0

• Tan ∝ =  0 / p

• Tan ∝  = 0

• ∝ = 0

2. When theta = 90 i.e. when the vector p and q r perpendicular to each other, then:

R = $\sqrt{p^{2} + q^{2} + 2pq cos}$ theta

R = $\sqrt{p^{2} + q^{2} + 2pq}$    ----------------------------[Cos 0 = 1]

  = $\sqrt{(p + q)^{2} }$

Here, Tan ^ -1  ∝ = q sin 90 / p + q cos 90

                            = q x 1 / p + 0

                            = q / p

                      ∝   = Tan^ -1 . q / p