A) \[\frac{3}{7}\]
B) \[\frac{7}{3}\]
C) 3
D) 7
Correct Answer: B
Solution :
[b] \[\because \frac{Projection\text{ }of\text{ }a\text{ }on\text{ }b}{Projection\text{ }of\text{ }b\text{ }on\text{ }a}=\frac{\frac{\overrightarrow{a}.\overrightarrow{b}}{\left| \overrightarrow{b} \right|}}{\frac{\overrightarrow{a}.\overrightarrow{b}}{\left| \overrightarrow{a} \right|}}=\frac{\left| \overrightarrow{a} \right|}{\overrightarrow{b}}\] Now \[\left| \overrightarrow{a} \right|=\sqrt{{{\left( 2 \right)}^{2}}+{{(-3)}^{2}}+{{\left( -6 \right)}^{2}}}=\sqrt{4+9+36}=\sqrt{49}=7\] \[\left| \overrightarrow{b} \right|=\sqrt{{{\left( -2 \right)}^{2}}+{{(-2)}^{2}}+{{\left( -1 \right)}^{2}}}=\sqrt{9}=7\] Hence, the required ratio\[=\frac{7}{3}\].
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