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Let
u
=
(
3
i
−
j
+
2
k
)
+
t
(
i
+
2
j
−
k
)
\mathbf{u}=(3\mathbf{i}-\mathbf{j}+2\mathbf{k})+t(\mathbf{i}+2\mathbf{j}-\mathbf{k})
u
=
(
3
i
−
j
+
2
k
)
+
t
(
i
+
2
j
−
k
)
…
Mathematics
Problem
Let
u
=
(
3
i
−
j
+
2
k
)
+
t
(
i
+
2
j
−
k
)
\mathbf{u}=(3\mathbf{i}-\mathbf{j}+2\mathbf{k})+t(\mathbf{i}+2\mathbf{j}-\mathbf{k})
u
=
(
3
i
−
j
+
2
k
)
+
t
(
i
+
2
j
−
k
)
and
v
=
2
i
−
j
+
2
k
\mathbf{v}=2\mathbf{i}-\mathbf{j}+2\mathbf{k}
v
=
2
i
−
j
+
2
k
. (i) Find the value of
t
t
t
for which the scalar projection of
u
\mathbf{u}
u
on
v
\mathbf{v}
v
equals
6
6
6
. (ii) For this value of
t
t
t
, determine the vector component of
u
\mathbf{u}
u
along
v
\mathbf{v}
v
.
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