# Ex 10.3, 17 - Chapter 10 Class 12 Vector Algebra

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Ex 10.3, 17 (Method 1) Show that the vectors 2 + , 3 5 , 3 4 4 form the vertices of a right angled triangle. Let A(2 + ), B( 3 5 ) C(3 4 4 ) We know that two vectors are perpendicular to each other, i.e have an angle of 90 between them , if their scalar product is zero. = ( 3 5 ) (2 + ) = 1 3 5 2 + 1 1 = (1 2) + ( 3 + 1) + ( 5 1) = 1 2 6 = (3 4 4 ) ( 3 5 ) = 3 4 4 1 + 3 + 5 = (3 1) + ( 4 + 3) + ( 4 + 5) = 2 1 + 1 = (2 + ) (3 4 4 ) = 2 1 + 1 3 + 4 + 4 = (2 3) + ( 1 + 4) + (1 + 4) = 1 + 3 + 5 Now, . = (2 1 + 1 ) . (-1 + 3 + 5 ) = (2 1) + ( 1 3) + (1 5) = ( 2) + ( 3) + 5 = 5 + 5 = 0 Since, . = 0 Therefore, is perpendicular to . Hence ABC is a right angled triangle Ex 10.3, 17 (Method 2) Show that the vectors 2 + , 3 5 , 3 4 4 form the vertices of a right angled triangle. Let A(2 + ), B( 3 5 ) C(3 4 4 ) Considering ABC as a right angled triangle, By Pythagoras theorem, AB2 = BC2 + CA2 or AB 2 = BC 2 + CA 2 = ( 3 5 ) (2 + ) = 1 3 5 2 + 1 1 = (1 2) + ( 3 + 1) + ( 5 1) = 1 2 6 = (3 4 4 ) ( 3 5 ) = 3 4 4 1 + 3 + 5 = (3 1) + ( 4 + 3) + ( 4 + 5) = 2 1 + 1 = (2 + ) (3 4 4 ) = 2 1 + 1 3 + 4 + 4 = (2 3) + ( 1 + 4) + (1 + 4) = 1 + 3 + 5 Now, Magnitude of = 1 2+ 2 2+ 6 2 = 1+4+36 = 41 Magnitude of = 22+ 1 2+1 = 4+1+1 = 6 Magnitude of = ( 1)2+32+52 = 1+9+25 = 35 Now, 2 + 2 = ( 6 )2 + ( 35 )2 = 6 + 35 = 41 = ( 41 )2 = 2 Thus, 2 = 2 + 2 So, ABC is a right angled triangle.

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.