Question

Prove that the vectors A=21+ j + k,B= 2i+j+2k and
C= i+ j +k can form the sides of a right angled triangle

Answer 1

Explanation:

$ab = \sqrt{ {(2 - 2)}^{2} + {(1 - 1)}^{2} + {(2 - 1)}^{2} } = \sqrt{1} = 1$

$bc = \sqrt{ {(1 - 2)}^{2} + {( 1 - 1)}^{2} + {(1 - 2)}^{2} } = \sqrt{2}$

$ca = \sqrt{ {(1 - 2)}^{2} + {(1 - 1)}^{2} + {(1 - 1)}^{2} } = \sqrt{1} = 1$

since

${(ab)}^{2} + {(ca)}^{2} = {(bc)}^{2}$

it is a right triangle