The three vectors A =3 i -2 j + k , B = i -3 j +5 k and C =2 i - j +4 k will form

Step-by-step solution

Given vectors are A = 3 i - 2 j + k , B = i - 3 j + 5 k , and C = 2 i - j + 4 k . Magnitudes are : | A | = 14 , | B | = 35 , and | C | = 21 . All pairs satisfy the triangle inequality, confirming a valid triangle. The squared magnitudes are : | A |^2 = 14 , | B |^2 = 35 , | C |^2 = 21 . Since 14 + 21 = 35 , the Pythagorean theorem holds: | A |^2 + | C |^2 = | B |^2 , indicating a right-angled triangle. The triangle is not equilateral or isosceles due to unequal side lengths. Conclusion : Right-angled triangle. Answ