Question

If a² + b² + c² = 16, p² + q² + r² = 25 and ap + bq + cr = 20, then the value of (a + b + c)/(p + q + r)

1. 2/3
2. 3/4
3. 4/5
4. 5/6

Answer 1

Correct Answer - Option 3 : 4/5

Calculation:

a² + b² + c² = 16

Put b = c = 0, then

a² = 16

⇒ a = 4

Similarly,

p² + q² + r² = 25

Put q = r = 0

p² = 25

⇒ p = 5

Now,

ap + bq + rc = 20

⇒ 4 × 5 + 0 + 0 = 20

⇒ 20 = 20 (satisfied)

Now,

(a + b + c)/(p + q + r)

⇒ 4/5