Question

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

Answer 1

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Answer:

• m = j +k
• n = 2i +k

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