Question

If a

=6-5. b= 6+5, c = 6+5.

d= 6-5 and e = V6 + V5, then which of the

Column II

following is a rational number?

9

b) abde

(d) cd

P. 105 and 120

1.

(a) abcde

196 and 38220

2.

24

(c) abc ​

Answer 1

Step-by-step explanation:

Here,

AB=

(5+1)

2

+(0−2)

2

+(−6+3)

2

=

49

=7

AC=

(0+1)

2

+(4−2)

2

+(1+3)

2

=

9

=3

by geometry , the bisector of∠BAC

will divide the side BC in the ration AB:AC i.e.,in the ratio 7:3 internally .Let the bisector of ∠BAC , meets the side BC at point D.

Therefore,D divides BC in the ratio 7:3

coordinates of D are

(

7+3

7×0+3×5

,

7+3

7×4+3×0

,

7+3

7×(−1)+3×(−6)

)

(

2

3

,

5

14

,−

3

5

)

Therefore, direction ratio of the bisector AD are

2

3

−(−1),

5

14

−2,

2

−5

+3i.e.

2

5

,

5

4

,

2

1

Hence , direction cosines of the bisector AD are

(

2

5

)

2

+(

5

4

)

2

+(

2

1

)

2

2

5

(

2

5

)

2

+(

5

4

)

2

+(

2

1

)

2

5

4

(

2

5

)

2

+(

5

4

)

2

+(

2

1

)

2

2

1

714

25

,

714

8

,

714

5

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