Find the value of k if the pts A \equiv \left(\right. 1 , 2 , - 1 \left.\right) , B \equiv \left(\right. 4 , - 2 , 4 \left.\right) and C \equiv \left(\right. 0 , 0 , k \left.\right) form a triangle right angled at C.

Engineering

Mathematics

Line of Greatest Slope

Question

Find the value of

k

if the pts

A \equiv (1, 2, - 1), B \equiv (4, - 2, 4)

and

C \equiv (0, 0, k)

form a triangle right angled at

C

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

D R S

B A \equiv (3. - 4, 5)

C A \equiv (1, 2, - 1 - K)

C B \equiv (4, - 2, 4 - K)

since

C A ⊥ C B

∴ \vec{C A} . \vec{C B} = 0

∴ (1) (4) + (2) (- 2) + (- 1 - K) (4 - K) = 0

\Rightarrow 4 - 4 + (K + 1) (K - 4) = 0

\Rightarrow (K + 1) (K - 4) = 0

\Rightarrow K = - 1

K = 4

Please subscribe our Youtube channel to unlock this solution.