A) \[1/7\]
B) \[-1/7\]
C) \[7\]
D) \[-7\]
Correct Answer: B
Solution :
Key Idea: The projection of vectors \[\overset{\to }{\mathop{\mathbf{a}}}\,\] on \[\overset{\to }{\mathop{\mathbf{b}}}\,\] is \[\frac{\overset{\to }{\mathop{\mathbf{a}}}\,\cdot \overset{\to }{\mathop{\mathbf{b}}}\,}{|\overset{\to }{\mathop{\mathbf{b}}}\,|}\] Let\[\overset{\to }{\mathop{\mathbf{a}}}\,=\widehat{\mathbf{i}}+3\widehat{\mathbf{j}}+\widehat{\mathbf{k}},\,\,\overset{\to }{\mathop{\mathbf{b}}}\,=2\widehat{\mathbf{i}}-3\widehat{\mathbf{j}}+6\widehat{\mathbf{k}}\] \[\therefore \]Projection of\[\overset{\to }{\mathop{\mathbf{a}}}\,\]on\[\overset{\to }{\mathop{\mathbf{b}}}\,=\frac{\overset{\to }{\mathop{\mathbf{a}}}\,\cdot \overset{\to }{\mathop{\mathbf{b}}}\,}{|\overset{\to }{\mathop{\mathbf{b}}}\,|}\] \[=\frac{(\widehat{\mathbf{i}}+3\widehat{\mathbf{j}}+\widehat{\mathbf{k}})\cdot (2\mathbf{\hat{i}}-3\widehat{\mathbf{j}}+6\mathbf{\hat{k}})}{\sqrt{4+9+36}}\] \[=\frac{2-9+6}{7}=-\frac{1}{7}\]
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