If veca and vecb are two unit vectors and θ is the angle between them, then the unit vector along their angular bisector is

Question

If veca and vecb are two unit vectors and θ is the angle between them, then the unit vector along their angular bisector is (A) ( veca- vecb/2 cos (θ)2) (B) ( veca+ vecb/2 cos (θ)2) (C) ( veca- vecb/cos (θ)2) (D) ( veca+ vecb/cos (θ)2)

Tardigrade Admin · Accepted Answer

Vector in the direction of angle bisector of veca and vecb is ( veca+ vecb/2) It has the magnitude cos (θ/2) ∴ Unit vector along the direction of angular bisector is ( veca+ vecb/2 cos (θ /2))

Q. If $a$ and $b$ are two unit vectors and $θ$ is the angle between them, then the unit vector along their angular bisector is

$\frac{a - b}{2 cos \frac{θ}{2}}$

$\frac{a + b}{2 cos \frac{θ}{2}}$

$\frac{a - b}{cos \frac{θ}{2}}$

$\frac{a + b}{cos \frac{θ}{2}}$

Vector in the direction of angle bisector of $a$ and $b$ is $\frac{a + b}{2}$
It has the magnitude $cos (θ /2)$
$∴$ Unit vector along the direction of angular bisector is
$\frac{a + b}{2 cos ( θ /2 )}$

Q. If a and b are two unit vectors and θ is the angle between them, then the unit vector along their angular bisector is

2cos2θ​a−b​

2cos2θ​a+b​

cos2θ​a−b​

cos2θ​a+b​