questionr
Early access
Exams
Joint Entrance Examination
Mathematics
Vector Algebra
Question 272
Question 272 of 379
Medium
MCQ
The sum of the distinct real values of
μ
\mu
μ
for which
μ
i
^
+
j
^
+
k
^
\mu\hat i+\hat j+\hat k
μ
i
^
+
j
^
+
k
^
,
i
^
+
μ
j
^
+
k
^
\hat i+\mu\hat j+\hat k
i
^
+
μ
j
^
+
k
^
,
i
^
+
j
^
+
μ
k
^
\hat i+\hat j+\mu\hat k
i
^
+
j
^
+
μ
k
^
are coplanar is:
A
-1
B
0
C
1
D
2
Check answer
Press A-D to select · Enter to check
Solutions · 1
Post your solution
Official solution
\[\begin{vmatrix}\mu&1&1\\1&\mu&1\\1&1&\mu\end{vmatrix}=0 \implies \mu(\mu^2-1)-(\mu-1)+(1-\mu)=0 \implies (1-\mu)(\mu^2+\mu-2)=0\] \[\mu=1,-2 \implies \text{sum}=1+(-2)=-1\]
Answer the question to unlock
Previous
Next