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Mathematics
Mathematics
Problem
Let
p
⃗
=
(
a
+
1
)
i
^
+
2
j
^
−
3
k
^
\vec p = (a+1)\hat i + 2\hat j - 3\hat k
p
=
(
a
+
1
)
i
^
+
2
j
^
−
3
k
^
and
q
⃗
=
2
i
^
+
(
a
−
2
)
j
^
+
6
k
^
\vec q = 2\hat i + (a-2)\hat j + 6\hat k
q
=
2
i
^
+
(
a
−
2
)
j
^
+
6
k
^
. a. (i) Find the value of
a
a
a
for which
p
⃗
\vec p
p
is perpendicular to
q
⃗
\vec q
q
. b. (ii) For this value of
a
a
a
, calculate the magnitude of
p
⃗
×
q
⃗
\vec p \times \vec q
p
×
q
.
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