2. Simplify.
(a) (2^0+ 4^-1) 2^2
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12th
Maths
Three Dimensional Geometry
Direction Cosines and Direction Ratios
A( - 1, 2, 3), B(5, 0, - 6)...
MATHS
A(−1, 2, 3), B(5, 0, −6), C(0, 4, −1) are three points. Show that the direction cosines of the bisectors of ∠BAC are proportional to (25, 8, 5) and (−11, 20, 23).
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ANSWER
A(−1,2,−3)B(5,0,−6)
C(0,4,−1)
D.R's of AB are
=(5−(−1),0−2,−6−(−3))
=(6,−2,−3)
D.R's of AC rule
=(0−(−1),4−2,−1−(−3))
=(1,2,2)
DC's of AB are
7
6
,
7
−2
,
7
−3
[∵
6
2
+(−2)
2
+(−3)
2
=7]
DC's of AC are
3
1
,
3
2
,
3
2
[∵
1
2
+2
2
+2
2
=3]
DC's of Bisector of ∠ BAC is proportional to
7
6
±
3
1
,
7
−2
±
3
2
,
7
−3
±
3
2
21
18±7
,
21
−6±14
,
21
−9±14
(25,8,5) and (11,−20,−23)
i.e (25,8,5) and (−11,20,23)
Answer:
2⁰ = 1 .
4-¹ = 1/4.
so (4+1/4)4.
Ans = 5