The values of a for which (8,−7,a),(5,2,4) and (6,−1,2) are collinear is given by

Engineering

Mathematics

Direction Cosines and Direction Ratio

theorem in space

Question

The values of a for which (8,−7,a),(5,2,4) and (6,−1,2) are collinear is given by

–2

–1

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

Ans ⇒ given, (8,–7,9), (5,2,4) & (6,–1,2) ax collinear.

Let A ≡ (8,–7,a), B ≡ (5,2,h), C ≡ (6,–1,2)

⇒ points A,B,C are collinear.

⇒ Dirction ratio of AB = AC

⇒ AB = [(5 – 8),(2 + 7),(h – a)] ⇒ [–3,9,4– a]

⇒ AC = [(6 – 8),(–1 + 7),(2 – a)] ⇒ [–2,6,2 – a])

from eq^ns(t),AB = AC

$\frac{- 3}{- 2} = \frac{9}{6} = \frac{4 - a}{2 - a}$

$\frac{3}{2} = \frac{h - a}{2 - a}$

3(2 – a) = 2(4 – a)

6 – 3a = 8 – 2a

–3a + 2a = 8 – 6

–a = 2

∴ a = –2