If the position vector of $ A \& B $ are $ \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-7 \widehat{\mathrm{k}} $ and $ 5 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+4 \widehat{\mathrm{k}} $, then the direction cosine of ABalong $ Y $-axis is

Question

If the position vector of $ A \& B $ are $ \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-7 \widehat{\mathrm{k}} $ and $ 5 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+4 \widehat{\mathrm{k}} $, then the direction cosine of ABalong $ Y $-axis is, $ \frac{4}{\sqrt{162}} $, $ -\frac{5}{\sqrt{162}} $, $ -5 $, 11

MARKS App · Accepted Answer

Given: OA → = i ^ + 3 j ^ - 7 k ^ and OB → = 5 i ^ - 2 j ^ + 4 k ^ AB → = OB → - OA → > ⇒ AB → = 5 i ^ - 2 j ^ + 4 k ^ - i ^ + 3 j ^ - 7 k ^ ⇒ AB → = 4 i ^ - 5 j ^ + 11 k ^ Y -axis, cos β = –5 16 + 25 + 121 = – 5 162

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