. If A = {1, 2, 3}, B = (3, 4, 5} then
ΑΔ Β =
[
A) {0} B) {1, 2} C) {7} D) none
frnds here delta means what ?
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Answers
Answer:
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
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