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Byju's Answer
Standard XII
Mathematics
Section Formula
In a Δ ABC,...
Question
In a
Δ
ABC,
→
A
B
=
6
→
i
+
3
→
j
+
3
→
k
;
→
A
C
=
3
→
i
−
3
→
j
+
6
→
k
. D and D' are points of tri-sections of sides BC. Find
→
A
D
and
→
A
D
′
.
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Solution
We have
→
B
C
=
→
A
C
−
→
A
B
or,
→
B
C
=
(
3
^
i
−
3
^
j
+
6
^
k
)
−
(
6
^
i
+
3
^
j
+
3
^
k
)
=
−
3
^
i
−
6
^
j
+
3
^
k
.
Now, according to the problem,
→
B
D
=
→
D
′
C
=
1
3
→
B
C
=
(
−
^
i
−
2
^
j
+
^
k
)
.
∴
→
A
D
=
→
B
D
−
→
B
A
=
→
B
D
+
→
A
B
=
5
^
i
+
^
j
+
4
^
k
.
And
→
A
D
′
=
→
A
C
−
→
D
′
C
=
4
^
i
−
^
j
+
5
^
k
.
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Similar questions
Q.
Equation of the plane through three points
A
,
B
,
C
with position vectors
−
6
→
i
+
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→
j
+
2
→
k
,
3
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−
2
→
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→
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Q.
In a quadrilateral
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D
,
→
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→
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B
∧
→
A
D
)
which is
2
π
3
,
15
∣
∣
→
A
C
∣
∣
=
3
∣
∣
→
A
B
∣
∣
=
5
∣
∣
→
A
D
∣
∣
then
cos
(
→
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A
∧
→
C
D
)
is :
Q.
The vectors
2
→
i
+
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→
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+
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→
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,
3
→
i
+
2
→
j
−
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→
k
, and
5
→
i
+
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→
j
+
→
k
form:
Q.
If
A
B
C
D
E
F
is a regular hexagon and
→
A
B
+
→
A
C
+
→
A
D
+
→
E
A
+
→
F
A
=
λ
→
A
B
, then
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=
Q.
If
A
B
C
D
E
F
is a regular hexagon and
→
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B
+
→
A
C
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→
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D
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=
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