Let A 1 → = 3 ,   A 2 → = 5   and A 1 → + A 2 → = 5 . The value of 2 A 1…

Let A1→=3, A2→=5  and A1→+A2→=5. The value of 2A1→+3A2→∙3A1→-2A2→ is:
  1. -112.5
  2. -118.5
  3. -106.5
  4. -99.5

Solution

A→1+A→2=5
A→1+A→22=25
A→12+A→22+2A→1A→2=25
9+25+2A→1∙A→2=25
A→1.A→2=-92
Now, 2A→1+3A→2∙3A→1-2A→2=6A→12-4A→1A→2+9A→1A→2-6A→22
=6.A→12+5A→1A→2-6A→22
=6×9+5-92-6×25
=54-452-150
= -118.5

Asked in: JEE Main 2019 (08 Apr Shift 2)

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