Verified Solution • 2025–26 Session moderate

QJEEM21Mafb62: JEE Main 2021 Physics - Class 11 JEEM21Mafb62 Solution: If and = 8, then is equal to :

If ∣a→∣=2,∣b→∣=5\left| {\overrightarrow a } \right| = 2,\left| {\overrightarrow b } \right| = 5 and ∣a→×b→∣\left| {\overrightarrow a \times \overrightarrow b } \right| = 8, then ∣a→. b→∣\left| {\overrightarrow a .\,\overrightarrow b } \right| is equal to :

Multiple Choice Options

  • A 6
  • B 4
  • C 3
  • D 5

Step-by-Step Verified Solution

∣a→∣=2,∣b→∣=5\left| {\overrightarrow a } \right| = 2,\left| {\overrightarrow b } \right| = 5

∣a→×b→∣=∣a→∣∣b→∣sin⁡θ=±8\left| {\overrightarrow a \times \overrightarrow b } \right| = \left| {\overrightarrow a } \right|\left| {\overrightarrow b } \right|\sin \theta = \pm 8

sin⁡θ=± 45\sin \theta = \pm \,{4 \over 5}

∴\therefore a→. b→=∣a→∣∣b→∣cos⁡θ\overrightarrow a .\,\overrightarrow b = \left| {\overrightarrow a } \right|\left| {\overrightarrow b } \right|\cos \theta

=10.(± 35)=±6= 10.\left( { \pm \,{3 \over 5}} \right) = \pm 6

∣a→. b→∣=6\left| {\overrightarrow a .\,\overrightarrow b } \right| = 6

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