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Exams
Joint Entrance Examination
Mathematics
3D Geometry
Question 295
Question 295 of 521
Medium
MCQ
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be distinct positive numbers. If the vectors
a
i
^
+
a
j
^
+
c
k
^
a\hat i+a\hat j+c\hat k
a
i
^
+
a
j
^
+
c
k
^
,
i
^
+
k
^
\hat i+\hat k
i
^
+
k
^
, and
c
i
^
+
c
j
^
+
b
k
^
c\hat i+c\hat j+b\hat k
c
i
^
+
c
j
^
+
b
k
^
are coplanar, then
c
c
c
is equal to:
A
2
(
1
a
+
1
b
)
2\left(\dfrac1a+\dfrac1b\right)
2
(
a
1
+
b
1
)
B
a
+
b
2
\dfrac{a+b}{2}
2
a
+
b
C
1
a
+
1
b
\dfrac1a+\dfrac1b
a
1
+
b
1
D
a
b
\sqrt{ab}
ab
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Solutions · 1
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Official solution
\[\begin{vmatrix}a&a&c\\1&0&1\\c&c&b\end{vmatrix}=0.\] \[a(0\cdot b-1\cdot c)-a(1\cdot b-1\cdot c)+c(1\cdot c-0\cdot c)=-ac-ab+ac+c^2=c^2-ab=0.\] \[c=\sqrt{ab}.\]
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