Question
Download Solution PDFयदि A = \(\rm 5 \hat i-2\hat j +4\hat k\) और B = \(\rm \hat i+3\hat j -7\hat k\) है, तो \(\rm |\vec{AB}|\) का मान क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
यदि \(\rm \vec A = x \hat i-y\hat j +z\hat k\) है, तो \(\rm |\vec A| = \sqrt {x^2 +y^2+z^2}\) है।
गणना:
दिया गया है A = \(\rm 5 \hat i-2\hat j +4\hat k\) और B = \(\rm \hat i+3\hat j -7\hat k\)
\(\rm \vec{AB} = \vec B - \vec A\)
\(\rm \vec{AB}\) = \(\rm \hat i+3\hat j -7\hat k - (5 \hat i-2\hat j +4\hat k)\)
\(\rm \vec{AB}\) = \(\rm -4\hat i+5\hat j -11\hat k\)
अब \(\rm |\vec {AB}| = \sqrt{(-4)^2 +5^2+(-11)^2}\)
\(\rm |\vec {AB}| = \sqrt{16 +25+121}\)
\(\rm |\vec {AB}| = \sqrt{162}\) = 9√2
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