AP EAMCET Engineering 22 Sep 2020 Shift 1 Paper

Let

→

c

be the unit vector along the angular bisector of

→

a

and

→

b

. Then, we have:

→

c

=‌

→ a + → b

| → a + → b |

Now, we need to simplify

→

a

+

→

b

. We can use the cosine rule to find the magnitude of

→

a

+

→

b

as follows:

|

→

a

+

→

b

|2=|

→

a

|2+|

→

b

|2+2|

→

a

||

→

b

|cos‌θSince

→

a

and

→

b

are unit vectors, we have |

→

a

|=|

→

b

|=1. Substituting this in the above equation, we get:

|

→

a

+

→

b

|2=2+2‌cos‌θ=4cos2‌

θ

2

Hence, we have:
|

→

a

+

→

b

|=2‌cos‌

θ

2

Now, substituting this in the expression for

→

c

, we get:

→

c

=‌

→ a + → b

| → a + → b |

=‌

→ a + → b

2‌cos‌ θ 2

Therefore, the unit vector along the angular bisector of

→

a

and

→

b

is:

→

c

=‌

→ a + → b

2‌cos‌ θ 2