Question

If Aˆ

and Bˆ

are two unit vectors and their resultant is also another unit vector Cˆ

. Find

angle between A

 and B​

Answer 1

Answer:

Let $\large\rm { \vec { a} \vec{b} }$ be two unit vectors whose sum is also a unit vector $\large\rm { \vec { c}}$

$\large\rm { \vec { a } + \vec {b} = \vec {c} .......(1) \ and \ \vec { |a| } = \vec {|b|} = \vec {|c| } = 1}$

Now magnitude of sum of $\large\rm { \vec { a} \vec{b} }$ is

$\large\rm { | \vec {a} + \vec {b} | = | \vec {a} |^{2} + |\vec {b} |^{2} + 2( \vec {a} \cdot \vec {b} ) }$

$\large\rm { → \vec {a} \cdot \vec {b} = - \frac {1}{2}}$

Magnitude of their difference is given b

$\large\rm { | \vec {a} - \vec {b} | = | \vec {a} |^{2} + |\vec {b} |^{2} + 2 \vec {a} \cdot \vec {b} }$

$\large\rm { → |a-b| = \sqrt {3} }$ ✓✓✓