1.

बिन्दुओं \( 2 \hat{i}-3 \hat{j}-\hat{k} \) तथा \( 8 \hat{i}-\hat{j}+3 \hat{k} \) को मिलाने वाली सरल रेख का समीकरण ज्ञात कीजिए।

Answer»

\(\vec r=\vec a+\lambda(\vec b-\vec a)\) 

where \(\vec a\) = 2\(\hat i\) - 3\(\hat j\) - \(\hat k\)

\(\vec b=8\hat i-\hat j+3\hat k\)

\(\therefore\) Equation of required line is

\(\vec r=\vec a+\lambda(\vec b-\vec a)\)

\((2\hat i-3\hat j-\hat k)\) + \(\lambda((8\hat i-\hat j+3\hat k)-(2\hat i-3\hat j-\hat k))\) 

 = \((2\hat i-3\hat j-\hat k)\) + \(\lambda((8-2)\hat i+(-1+3)\hat j+(3-(-1))\hat k)\) 

 = \((2\hat i-3\hat j-\hat k)\) + \(\lambda(6\hat i+2\hat j+4\hat k)\)



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