Show that the points A, B and C with position vectors,, respectively form the vertices of a right angled triangle.

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Solution

Position vectors of points A, B, and C are respectively given as:

${|\vec{AB}|}^{2} + {|\vec{CA}|}^{2} = 35 + 6 = 41 = {|\vec{BC}|}^{2}$

Hence, ABC is a right-angled triangle.

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Show that the points A, B and C with position vectors,, respectively form the vertices of a right angled triangle.

Position vectors of points A, B, and C are respectively given as: AB→2+CA→2=35+6=41=BC→2 Hence, ABC is a right-angled triangle.

Position vectors of points A, B, and C are respectively given as:

${|\vec{AB}|}^{2} + {|\vec{CA}|}^{2} = 35 + 6 = 41 = {|\vec{BC}|}^{2}$

Hence, ABC is a right-angled triangle.