Given that vector p=i+2j-2k and q=2i-j+2k, find two vectors m and m satisfying the condition; m is perpendicular to p

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Step-by-step explanation:

There are an infinite number of possibilities. Any vector whose dot-product with p is zero will be perpendicular to p.

Let m = 0i +1j +ak. Then we require ...

  m·p = 0 = 0×1 +1×2 +a(-2)   ⇒   0 = 2 -2a   ⇒   a = 1

m = 0i +1j +1k

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Let n = 2i +0j +bk

  n·p = 0 = 2×1 +0×2 +b(-2)   ⇒   2 -2b = 0   ⇒   b = 1

n = 2i +0j +1k

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step-by-step explanation: