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CBSE Class 12 Math 2023 All Sets Solved Paper

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Question : 4 of 20
Marks: +1, -0
Unit vector PQ→,\overrightarrow{PQ}, where coordinates of P and Q respectively are (2, 1, -1) and (4, 4, -7), is
Solution:  
PQ→=OQ→−OP→\overrightarrow{PQ}=\overrightarrow{OQ}-\overrightarrow{OP}
=(4i^+4j^−7k^)−(2i^+j^−k^)=(4\hat{i}+4\hat{j}-7\hat{k})-(2\hat{i}+\hat{j}-\hat{k})
=2i^+3j^−6k^=2\hat{i}+3\hat{j}-6\hat{k}
∣PQ→∣=22+32+(−6)2=7|\overrightarrow{PQ}|=\sqrt{2^2+3^2+(-6)^2}=7
Unit vector along PQ→\overrightarrow{PQ} is
a^=PQ→∣PQ→∣\hat{a}=\frac{\overrightarrow{PQ}}{|\overrightarrow{PQ}|}
=2i^7+3j^7−6k^7=\frac{2\hat{i}}{7}+\frac{3\hat{j}}{7}-\frac{6\hat{k}}{7}
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