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Mathematics
Problem
Let
a
=
3
i
^
+
4
j
^
−
12
k
^
\mathbf{a}=3\hat{i}+4\hat{j}-12\hat{k}
a
=
3
i
^
+
4
j
^
−
12
k
^
and let the scalar
k
=
−
3
2
.
k=-\dfrac{3}{2}.
k
=
−
2
3
.
(a) Find the vector
k
a
.
k\mathbf{a}.
k
a
.
(b) Compute
∣
a
∣
|\mathbf{a}|
∣
a
∣
and
∣
k
a
∣
.
|k\mathbf{a}|.
∣
k
a
∣.
(c) Determine the ratio
∣
k
a
∣
∣
a
∣
.
\dfrac{|k\mathbf{a}|}{|\mathbf{a}|}.
∣
a
∣
∣
k
a
∣
.
(d) State the angle between
a
\mathbf{a}
a
and
k
a
.
k\mathbf{a}.
k
a
.
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