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Mathematics
Mathematics
Problem
The position vector of a point
P
P
P
is
r
=
x
i
^
+
y
j
^
+
z
k
^
\mathbf{r} = x\hat{i} + y\hat{j} + z\hat{k}
r
=
x
i
^
+
y
j
^
+
z
k
^
, where
x
,
y
,
z
∈
N
x, y, z \in \mathbb{N}
x
,
y
,
z
∈
N
and
a
=
i
^
+
2
j
^
+
k
^
\mathbf{a} = \hat{i} + 2\hat{j} + \hat{k}
a
=
i
^
+
2
j
^
+
k
^
. If
r
⋅
a
=
20
\mathbf{r} \cdot \mathbf{a} = 20
r
⋅
a
=
20
, then the number of possible position of
P
P
P
is a. 81 b. 49 c. 100 d. 36
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