Verified Solution • 2025–26 Session moderate

QJEEM22Mac18a: JEE Main 2022 Physics - Class 11 JEEM22Mac18a Solution: Let and . Then the number of vectors such that and {1, 2,…

Let a→=i^+j^−k^\overrightarrow a = \widehat i + \widehat j - \widehat k and c→=2i^−3j^+2k^\overrightarrow c = 2\widehat i - 3\widehat j + 2\widehat k . Then the number of vectors b→\overrightarrow b such that b→×c→=a→\overrightarrow b \times \overrightarrow c = \overrightarrow a and ∣b→∣∈|\overrightarrow b | \in {1, 2, ........, 10} is :

Multiple Choice Options

  • A 0
  • B 1
  • C 2
  • D 3

Step-by-Step Verified Solution

a→=i^+j^−k^\overrightarrow a = \widehat i + \widehat j - \widehat k

c→=2i^−3j^+2k^\overrightarrow c = 2\widehat i - 3\widehat j + 2\widehat k

Now, b→×c→=a→\overrightarrow b \times \overrightarrow c = \overrightarrow a

c→ . (b→×c→)=c→ . a→\overrightarrow c \,.\,(\overrightarrow b \times \overrightarrow c ) = \overrightarrow c \,.\,\overrightarrow a

c→ . a→=0\overrightarrow c \,.\,\overrightarrow a = 0

⇒(i^+j^−k^)(2i^−3j^+2k^)=0\Rightarrow (\widehat i + \widehat j - \widehat k)(2\widehat i - 3\widehat j + 2\widehat k) = 0

=2−3−2=0= 2 - 3 - 2 = 0

⇒−3=0\Rightarrow - 3 = 0 (Not possible)

⇒\Rightarrow No possible value of b→\overrightarrow b is possible.

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring