Question

If P Vector = Px i^ + Py j^ + Pz k^ and Q Vector = Qx i^ + Qy j^ + Qz k^ then find P Vector × Q Vector​

Answer 1

Answer:

Let two vectors P and Q be P=Pxi+Pyj+Pzk and Q=Qxi+Qyj+Qzk. Now P+Q = (Px+Qx)i+(Py+Qy)j+Pz+Qz)k and P-Q=(Px-Qx)i+(Py-Qy)j+(Pz-Qz)k. The resultant of P+Q and P-Q is 2(Pxi+Pyj+Pzk) which has double the length of vector P same direction as P. So the angle between P and the resultant of P+Q and P-Q is zero.

If

P = a1ı⃗ +b1ȷ⃗

Q = a2ı⃗ +b2ȷ⃗

The angle between P and P+Q is:

tan−1b1+b2a1+a2−tan−1b1a1

The angle between P and P-Q is:

tan−1b1−b2a1−a2−tan−1b1a1