Question

The number of integral values of p, such that the angle between vectors →a=p^i+3^j−7^k and →b=p^i−p^j+4^k is obtuse, is

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Solution

We know, cosθ=→a⋅→b|→a||→b|<0 (∵ angle between both vectors is obtuse) ⇒p2−3p−28√p2+9+49⋅√p2+p2+16<0⇒p2−3p−28<0⇒(p−7)(p+4)<0p∈(−4,7) So, number of integral values of p are 10.

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