Verified Solution • 2025–26 Session moderate

QJEEM22Ma2cb3: JEE Main 2022 Physics - Class 11 JEEM22Ma2cb3 Solution: If , and are coplanar vectors and , , then is equal to…

If a→=2i^+j^+3k^\overrightarrow a = 2\widehat i + \widehat j + 3\widehat k , b→=3i^+3j^+k^\overrightarrow b = 3\widehat i + 3\widehat j + \widehat k and c→=c1i^+c2j^+c3k^\overrightarrow c = {c_1}\widehat i + {c_2}\widehat j + {c_3}\widehat k are coplanar vectors and a→ . c→=5\overrightarrow a \,.\,\overrightarrow c = 5 , b→⊥c→\overrightarrow b \bot \overrightarrow c , then 122(c1+c2+c3)122({c_1} + {c_2} + {c_3}) is equal to ___________.

Step-by-Step Verified Solution

2C1+C2+3C3=52{C_1} + {C_2} + 3{C_3} = 5 ...... (i)

3C1+3C2+C3=03{C_1} + 3{C_2} + {C_3} = 0 ...... (ii)

[a→b→c→]=|213331C1C2C3|

=2(3C3−C2)−1(3C3−C1)+3(3C2−3C1)= 2(3{C_3} - {C_2}) - 1(3{C_3} - {C_1}) + 3(3{C_2} - 3{C_1})

=3C3+7C2−8C1= 3{C_3} + 7{C_2} - 8{C_1}

⇒8C1−7C2−3C3=0\Rightarrow 8{C_1} - 7{C_2} - 3{C_3} = 0 ...... (iii)

C1=10122,C2=−85122,C3=225122{C_1} = {{10} \over {122}},{C_2} = {{ - 85} \over {122}},{C_3} = {{225} \over {122}}

So 122(C1+C2+C3)=150122({C_1} + {C_2} + {C_3}) = 150

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