Question

Show that a = 2i -j+k, b = i - 3j - 5k and = 3i -4j-4k taken in order form the sides of a right angled triangle. Also find the remaining angles of the triangle.​

Answer 1

a= 2i - j + k, b = i - 3j - 5k , c = 3i - 4j - 4k

let us find |a| , |b|. and |c|

| a | = √(4 + 1 + 1) => √6

| b | = √(1 + 9 + 25) => √35

| c | = √(9 + 16 + 16) => √41

now |a|² = 6 , |b|² = 35 and |c|² = 41

|a| ² + |b|² = |c|² for a right angled ∆

6 + 35 = 41 as it satisfies Pythagoras theorem, the

given three vectors taken in order form a right angled

∆

a and b form two sides containing right angle and c

forms hypotenuse.