Last updated at April 21, 2021 by Teachoo

Transcript

Ex 10.3, 14 If either vector ๐ โ = 0 โ or ๐ โ = 0 โ, then ๐ โ. ๐ โ = 0 But the converse need not be true. justify your answer with an example. Converse: If ๐ โ . ๐ โ = 0, then either ๐ โ = 0 โ or ๐ โ = 0 โ Let ๐ โ = ๐ ฬ + ๐ ฬ + ๐ ฬ = 1๐ ฬ + 1๐ ฬ + 1๐ ฬ and ๐ โ = ๐ ฬ + ๐ ฬ - 2๐ ฬ = 1๐ ฬ + 1๐ ฬ โ 2๐ ฬ ๐ โ . ๐ โ = 1.1 + 1.1 + 1(โ2) = 1 + 1 โ 2 = 0 Hence, ๐ โ . ๐ โ = 0 but ๐ โ โ 0 โ and ๐ โ โ 0 โ Thus, the converse need not be true.

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.