Ex 10.4, 6 Given that π β . π β = 0 and π β Γ π β = 0 β . What can you conclude about the vectors π β and π β ? π β . π β = 0
π β . π β = |π β ||π β | cos ΞΈ
β |π β ||π β | cos ΞΈ = 0
β |π β | = 0 or |π β | = 0
or cos ΞΈ = 0 i.e. ΞΈ = 90Β°
π β Γ π β = 0
π β Γ π β = |π β ||π β | sin ΞΈ π Μ
β |π β ||π β | sinΞΈ π Μ = 0 β
β |π β | = 0 or |π β | = 0
or sin ΞΈ = 0 i.e. ΞΈ = 0Β°
Given,
Since ΞΈ = cannot be equal to 0Β° and 90Β° simultaneously,
So, sin ΞΈ = 0 or cos ΞΈ = 0 is not possible.
Thus, either |π β | = 0 or |π β | = 0
Hence, either π β = 0 β or π β = 0 β .

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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