Question

The angle between A=5i-5j and B= 10i-10j

Answer 1

Answer:

45° draw the graph and point place on it measure the angle made by line joining the two points with x axis

Answer 2

Answer:

$\bigstar{\bold{Angle\:between\:the\:vectors=0^{o}}}$

Explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• $\vec{A}=5\hat{i}-5\hat{j}$

• $\vec{B}=10\hat{i}-10\hat{j}$

$\Large{\underline{\underline{\bf{To\:find:}}}}$

• Angle between the vectors

$\Large{\underline{\underline{\bf{Solution:}}}}$

→ Angle between two vectors is given by the formula

  $cos\theta=\dfrac{\vec{A}.\vec{B}}{|A||B|}$

→ $\vec{A}.\vec{B}=5\times10+-5\times-10$

  $\vec{A}.\vec{B}=100$

→$|A|=\sqrt{5^{2} +5^{2} }$

 $|A|=\sqrt{50}$

→$|B|=\sqrt{10^{2}+10^{2} }$

 $|B|=\sqrt{200}$

→ Substituting these datas in the formula we get

   $cos\theta=\dfrac{100}{\sqrt{50}\times \sqrt{200} }$

  $cos\theta=\dfrac{100}{\sqrt{50} \times2\sqrt{50} }$

  $cos\theta=\dfrac{50}{50} =1$

  θ = 0°

$\boxed{\bold{Angle\:between\:the\:vectors=0^{o}}}$

$\Large{\underline{\underline{\bf{Notes:}}}}$

→ The angle between two vectors is given by

   $cos\theta=\dfrac{\vec{A}.\vec{B}}{|A||B|}$