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Mathematics
Mathematics
Problem
Consider
A
⃗
=
a
i
^
−
2
j
^
+
4
k
^
\vec A = a\hat i - 2\hat j + 4\hat k
A
=
a
i
^
−
2
j
^
+
4
k
^
and
B
⃗
=
2
i
^
+
j
^
+
k
^
\vec B = 2\hat i + \hat j + \hat k
B
=
2
i
^
+
j
^
+
k
^
. The vector
A
⃗
\vec A
A
is required to be perpendicular to
B
⃗
\vec B
B
, and the vector
C
⃗
=
A
⃗
+
B
⃗
\vec C = \vec A + \vec B
C
=
A
+
B
must be parallel to
2
i
^
−
2
j
^
+
10
k
^
2\hat i - 2\hat j + 10\hat k
2
i
^
−
2
j
^
+
10
k
^
. Which value of
a
a
a
satisfies both conditions? a)
−
2
-2
−
2
b)
1
1
1
c)
−
1
-1
−
1
d)
2
2
2
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