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Mathematics
Mathematics
Problem
The line whose vector equation are
r
=
2
i
^
−
3
j
^
+
7
k
^
+
λ
(
2
i
^
+
p
j
^
+
5
k
^
)
\mathbf{r} = 2\hat{i} - 3\hat{j} + 7\hat{k} + \lambda(2\hat{i} + p\hat{j} + 5\hat{k})
r
=
2
i
^
−
3
j
^
+
7
k
^
+
λ
(
2
i
^
+
p
j
^
+
5
k
^
)
and
r
=
i
^
+
2
j
^
+
3
k
^
+
μ
(
3
i
^
−
p
j
^
+
p
k
^
)
\text{and } \mathbf{r} = \hat{i} + 2\hat{j} + 3\hat{k} + \mu(3\hat{i} - p\hat{j} + p\hat{k})
and
r
=
i
^
+
2
j
^
+
3
k
^
+
μ
(
3
i
^
−
p
j
^
+
p
k
^
)
are perpendicular for all values of
λ
\lambda
λ
and
μ
\mu
μ
if
p
p
p
equals to a. -1 b. 2 c. 5 d. 6
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