VectorHard
Question
If 
are non-coplanar vectors and p, q are real numbers, then the equality
= 0 holds for
are non-coplanar vectors and p, q are real numbers, then the equality = 0 holds forOptions
A.exactly one value of (p, q)
B.exactly two values of (p, q)
C.more than two but not all values of (p , q)
D.all values of (p, q)
Solution
(3p2 - pq + 2q2) 
= 0
But ≠ 0
3p2 - pq + 2q2 = 0
2p2 + p2 - pq +
= 0 ⇒ 2p2 + 
q2 = 0
⇒ p = 0, q = 0, p =
This possible only when p = 0, q = 0 exactly one value of (p, q)
= 0But
≠ 03p2 - pq + 2q2 = 0
2p2 + p2 - pq +
= 0 ⇒ 2p2 + q2 = 0⇒ p = 0, q = 0, p =
This possible only when p = 0, q = 0 exactly one value of (p, q)
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