Let O be the origin, and −−→OX,−−→OY,−−→OZ be three unit vectors in the directions of the sides −−→QR,−−→RP,−−→PQ, respectively, of a triangle PQR. If the triangle PQR varies, then the minimum value of cos(P+Q)+cos(Q+R)+cos(R+P)
Let two tangents are drawn to the curve y2−4(x+y)=3sinθ+4cosθ−15, x,y,θ∈R from the origin whose slopes are m1,m2. If the vertex of the curve is at maximum distance from the origin, then the value of ∣∣∣1m1m2∣∣∣ is