1e:I[80107,["/_next/static/chunks/235ad55241b6443f.js","/_next/static/chunks/8337ab1f037b6654.js","/_next/static/chunks/c9e933b5fd1a0afc.js","/_next/static/chunks/848a330faa2461ac.js","/_next/static/chunks/9f2942e368a262d2.js","/_next/static/chunks/92f9e11244990470.js","/_next/static/chunks/a8b867fbb1dfca1a.js","/_next/static/chunks/1100f0390a901fa7.js","/_next/static/chunks/bbe6bd9d3c7b0355.js","/_next/static/chunks/a82195c3e5de7dd4.js"],"default"] 1f:I[76763,["/_next/static/chunks/235ad55241b6443f.js","/_next/static/chunks/8337ab1f037b6654.js","/_next/static/chunks/c9e933b5fd1a0afc.js","/_next/static/chunks/848a330faa2461ac.js","/_next/static/chunks/9f2942e368a262d2.js","/_next/static/chunks/92f9e11244990470.js","/_next/static/chunks/a8b867fbb1dfca1a.js","/_next/static/chunks/1100f0390a901fa7.js","/_next/static/chunks/bbe6bd9d3c7b0355.js","/_next/static/chunks/a82195c3e5de7dd4.js"],"default"] 1d:T433,{"@context":"https://schema.org","@graph":[{"@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https://www.divinejee.com"},{"@type":"ListItem","position":4,"name":"Let lambda be an integer If the shortest distance between th","item":"https://www.divinejee.com/question/let-lambda-be-an-integer-if-the-shortest-distance-between-the-lines-x-lambda-2y-1-2z-and-x-y"}]},{"@type":"QAPage","mainEntity":{"@type":"Question","name":"Question Let lambda be an integer If the shortest distance between th on Topic","text":"Let $\\lambda$ be an integer. If the shortest distance between the lines

x $-$ $\\lambda$ = 2y $-$ 1 = $-$2z and x = y + 2$\\lambda$ = z $-$ $\\...","answerCount":1,"upvoteCount":0,"datePublished":"2026-01-16","author":{"@type":"Organization","name":"DivineJEE"},"acceptedAnswer":{"@type":"Answer","text":"Check the detailed solution on the page.","upvoteCount":0,"url":"https://www.divinejee.com/question/let-lambda-be-an-integer-if-the-shortest-distance-between-the-lines-x-lambda-2y-1-2z-and-x-y"}}}]}20:T4bd,$${{x - \lambda } \over 1} = {{y - {1 \over 2}} \over {{1 \over 2}}} = {z \over { - {1 \over 2}}}$$

$${{x - \lambda } \over 2} = {{y - {1 \over 2}} \over 1} = {2 \over { - 1}}$$ ....... (1)

Point on line = $$\left( {\lambda ,{1 \over 2},0} \right)$$

$${x \over 1} = {{y + 2\lambda } \over 1} = {{z - \lambda } \over 1}$$ ....... (2)

Point on line = $$(0, - 2\lambda ,\lambda )$$

Distance between skew lines $$ = {{\left[ {{{\overrightarrow a }_2} - {{\overrightarrow a }_1}{{\overrightarrow b }_1}{{\overrightarrow b }_2}} \right]} \over {\left| {{{\overrightarrow b }_1} \times {{\overrightarrow b }_2}} \right|}}$$

$$\left| {\matrix{ \lambda & {{1 \over 2} + 2\lambda } & { - \lambda } \cr 2 & 1 & { - 1} \cr 1 & 1 & 1 \cr } } \right|$$

$$\overline {\left| {\matrix{ {\widehat i} & {\widehat j} & {\widehat k} \cr 2 & 1 & { - 1} \cr 1 & 1 & 1 \cr } } \right|} $$

$$ = {{\left| { - 5\lambda - {3 \over 2}} \right|} \over {\sqrt {14} }} = {{\sqrt 7 } \over {2\sqrt 2 }}$$

$$ = |10\lambda + 3| = 7 \Rightarrow \lambda = - 1$$

$$ \Rightarrow |\lambda | = 1$$