Verified Solution • 2025–26 Session moderate

QJEEM20Ma5e44: JEE Main 2020 Physics - Class 11 JEEM20Ma5e44 Solution: The lines and

The lines
r→=(i^−j^)+l(2i^+k^)\overrightarrow r = \left( {\widehat i - \widehat j} \right) + l\left( {2\widehat i + \widehat k} \right) and
r→=(2i^−j^)+m(i^+j^+k^)\overrightarrow r = \left( {2\widehat i - \widehat j} \right) + m\left( {\widehat i + \widehat j + \widehat k} \right)

Multiple Choice Options

  • A do not intersect for any values of ll and m
  • B intersect for all values of ll and m
  • C intersect when ll = 2 and m = 12{1 \over 2}
  • D intersect when ll = 1 and m = 2

Step-by-Step Verified Solution

L1 = r→=(i^−j^)+l(2i^+k^)\overrightarrow r = \left( {\widehat i - \widehat j} \right) + l\left( {2\widehat i + \widehat k} \right)

= i^(1+2l)+j^(−1)+k^(l)\widehat i\left( {1 + 2l} \right) + \widehat j\left( { - 1} \right) + \widehat k\left( l \right)

L2 = r→=(2i^−j^)+m(i^+j^+k^)\overrightarrow r = \left( {2\widehat i - \widehat j} \right) + m\left( {\widehat i + \widehat j + \widehat k} \right)

= i^(2+m)+j^(m−1)+k^(−m)\widehat i\left( {2 + m} \right) + \widehat j\left( {m - 1} \right) + \widehat k\left( { - m} \right)

Equating coefficient of i^\widehat i , j^\widehat j and k^\widehat k of L1 and L2

2l + 1 = m + 2 ... (1)

–1 = –1 + m ...(2)

l = –m ...(3)

from (ii) m = 0

from (iii) ll = 0

These values of m and ll do not satisfy equation (1).

Hence the two lines do not intersect for any values of ll and m.

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