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(i) You are given that ?⃗ =〈2 , 3 ,4〉 and ? = 〈−1 , −1...

(i) You are given that ?⃗ =〈2 , 3 ,4〉 and ? = 〈−1 , −1 , 4〉 .

Find a vector ? that is orthogonal to both ?⃗ and ? .

Also find the equation of the plane that is determined by both ?⃗ and ?.

(ii) If ?⃗ and ? are vectors in ?? prove algebraically that ‖ ?⃗ + ? ‖ ≤ ‖ ?⃗ ‖ + ‖ ? ‖ . Interpret the result geometrically.

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