Given that a-b -0 and a - b -0 - What can you conclude about the vectors a and b -

Given that a.b = 0 Then, either |a| = 0 or |b| = 0 or a ⊥ b (in case a and b are non zero) and if a × b = 0 then either |a| = 0 or |b| = 0 or a || b (in case a ...

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Standard XII

Mathematics

Cross Product of Two Vectors

Given that a....

Question

Given that $a . b = 0$ and $a \times b = 0$ . What can you conclude about the vectors a and b?

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Solution

Given that a.b = 0
Then, either |a| = 0 or |b| = 0 or $a ⊥ b$ (in case a and b are non-zero) and if $a \times b = 0$ then either |a| = 0 or |b| = 0 or a || b (in case a and b are non zero). But a and b cannot be perpendicular and parallel simultaneously.
Hence, $| a | = 0$ or $| b | = 0$

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If a.a = 0 and a.b = 0, then what can be conclude about the vector b?

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Given that a.b=0 and a×b=0. What can you conclude about the vectors a and b?

Given that a.b = 0 Then, either |a| = 0 or |b| = 0 or a⊥b (in case a and b are non-zero) and if a×b=0 then either |a| = 0 or |b| = 0 or a || b (in case a and b are non zero). But a and b cannot be perpendicular and parallel simultaneously. Hence, |a|=0 or |b|=0

Given that $a . b = 0$ and $a \times b = 0$ . What can you conclude about the vectors a and b?

Given that a.b = 0
Then, either |a| = 0 or |b| = 0 or $a ⊥ b$ (in case a and b are non-zero) and if $a \times b = 0$ then either |a| = 0 or |b| = 0 or a || b (in case a and b are non zero). But a and b cannot be perpendicular and parallel simultaneously.
Hence, $| a | = 0$ or $| b | = 0$