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Question : 67 of 120
Marks:
+1,
-0
Solution:
Given,
|p+q|=√3⇒|p+q|2=(√3)2
⇒‌‌|p|2+|q|2+2p⋅q=3 ( ∵ p and q are non-collinear unit vectors, i.e.,
|p|=|q|=1) ⇒‌‌1+1+2p⋅q=3 ⇒‌‌p⋅q=‌......(i)
Now,
(2p−3q)⋅(3p+q) =6|p|2−9p⋅q+2p⋅q−3|q|2
=6(1)−7p⋅q−3(1) =3−7(‌)  [from Eq.(i)]
=−
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