| Statement I If \[a=2\hat{i}+3\hat{j}-\hat{k},b=-\hat{i}+3\hat{j}+4\hat{k},\] then projection of a on \[b=\frac{3}{\sqrt{26}}.\] |
| Statement II Projection of p on \[q=\frac{p\cdot q}{|q|}\] |
A) Both Statement I and Statement II are true and the Statement II is the correct explanation of the Statement I
B) Both Statement I and Statement II are true but the Statement II is not the correct explanation of the Statement I
C) Statement I is true but Statement II is false
D) Statement I is false but Statement II is true
Correct Answer: A
Solution :
From statements, vectors a and b are given then projection of a on \[b=\frac{a\cdot b}{|b|}\] \[=\frac{(2\hat{i}+3\hat{j}-\hat{k})\cdot (-\hat{i}+3\hat{j}+4\hat{k})}{\sqrt{{{(-1)}^{2}}+{{(3)}^{2}}+{{(4)}^{2}}}}\] \[=\frac{-2+9-4}{\sqrt{26}}=\frac{3}{\sqrt{26}}\] So, Statement I and Statement II both are true and Statement II is the correct explanation of the Statement I.
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