Question

P+Q+R=0 and ।P। = 8. ।Q। = 15 and ।R। =17angle between P and Qis​

Answer 1

Given :-

• P + Q + R = 0

• | P | = 8
• | Q | = 15
• | R | = 17

To find :-

• Angle between P and Q , θ = ?

Knowledge required :-

• Formula to find the magnitude of resultant of two vectors

magnitude of resultant of two vectors M and N is given by

| M + N |² = M² + N² + 2 MN cos θ

( where M , N are magnitudes of two vectors M and N  and θ is the angle between vectors M and N )

Solution :-

As given

↣   P + Q + R = 0

↣   P + Q = - R

so,

↣   | P + Q | = | - R |

↣   | P + Q |² = | - R |²

using formula for calculating magnitude of resultant of two vectors

↣ P² + Q² + 2 PQ cos θ = R²

↣ (8)² + (15)² + 2 (8)(15) cos θ = (17)²

↣ 64 + 225 + 240 cos θ = 289

↣ 240 cos θ = 289 - 64 - 225

↣ 240 cos θ = 0

↣ cos θ = 0

↣ θ = 90°

Therefore,

Angle between vectors P and Q is 90 degrees .

Note : In the Answer Bold letters P and Q are representing vectors and simple letters P and Q are representing magnitude of vectors P and Q.