MHT CET · Physics · Mathematics in Physics
Two vectors of same magnitude have a resultant equal to either of the two vectos. The angle between two vectors is
- A \(\operatorname{cos}^{-1}(-0 \cdot 3)\)
- B \(\cos ^{-1}(-0-6)\)
- C \(\operatorname{cos}^{-1}(-0 \cdot 4)\)
- D \(\operatorname{cos}^{-1}(-0 \cdot 5)\)
Answer & Solution
Correct Answer
(D) \(\operatorname{cos}^{-1}(-0 \cdot 5)\)
Step-by-step Solution
Detailed explanation
This is an important result to remember. Two vectors at 120 degree produce a vector equal to their magnitude. Let their magnitude be a,
\(\text {Resultant }=a=\sqrt{\left(a^{2}+a^{2}+2 \times a \times a \times \cos \theta\right)}=\) \(a \sqrt{(2+2 \cos \theta)} \Rightarrow \cos \theta=-\frac{1}{2}\)
\(\Rightarrow \theta=120^{0}\)
\(\text {Resultant }=a=\sqrt{\left(a^{2}+a^{2}+2 \times a \times a \times \cos \theta\right)}=\) \(a \sqrt{(2+2 \cos \theta)} \Rightarrow \cos \theta=-\frac{1}{2}\)
\(\Rightarrow \theta=120^{0}\)
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