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Mathematics
Problem
Assertion:
a
=
i
^
+
p
j
^
+
2
k
^
\mathbf{a} = \hat{i} + p\hat{j} + 2\hat{k}
a
=
i
^
+
p
j
^
+
2
k
^
and
b
=
2
i
^
+
3
j
^
+
q
k
^
\mathbf{b} = 2\hat{i} + 3\hat{j} + q\hat{k}
b
=
2
i
^
+
3
j
^
+
q
k
^
are parallel vectors, if
p
=
3
2
p = \frac{3}{2}
p
=
2
3
and
q
=
4
q = 4
q
=
4
. Reason:
a
=
a
1
i
^
+
a
2
j
^
+
a
3
k
^
\mathbf{a} = a_1\hat{i} + a_2\hat{j} + a_3\hat{k}
a
=
a
1
i
^
+
a
2
j
^
+
a
3
k
^
and
b
=
b
1
i
^
+
b
2
j
^
+
b
3
k
^
\mathbf{b} = b_1\hat{i} + b_2\hat{j} + b_3\hat{k}
b
=
b
1
i
^
+
b
2
j
^
+
b
3
k
^
are parallel
a
1
b
1
=
a
2
b
2
=
a
3
b
3
\frac{a_1}{b_1} = \frac{a_2}{b_2} = \frac{a_3}{b_3}
b
1
a
1
=
b
2
a
2
=
b
3
a
3
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