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Byju's Answer
Standard XII
Mathematics
Definition of a Determinant
If the points...
Question
If the points
(
5
,
4
,
2
)
,
(
8
,
k
,
−
7
)
and
(
6
,
2
,
−
1
)
are collinear, then
k
=
A
−
2
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B
2
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C
10
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D
1
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Solution
The correct option is
A
−
2
For collinear points in
3
−
Dimensional.
Their determinant should be zero.
∣
∣ ∣
∣
5
4
2
8
k
−
7
6
2
−
1
∣
∣ ∣
∣
=
0
⟹
5
(
−
k
+
14
)
−
4
(
−
8
+
42
)
+
2
(
16
−
6
K
)
=
0
⟹
−
17
k
−
34
=
0
⟹
k
=
−
2
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