Exter (a) Let A = (-2,0, 1), B= (0, 4, 1) and C= (-1,2,0) be points in R³. (1) Find a general form of the equation for t

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Exter A Let A 2 0 1 B 0 4 1 And C 1 2 0 Be Points In R 1 Find A General Form Of The Equation For T 1 (47.43 KiB) Viewed 36 times

Exter (a) Let A = (-2,0, 1), B= (0, 4, 1) and C= (-1,2,0) be points in R³. (1) Find a general form of the equation for the plane P containing A, B and C. (ii) Find parametric equations for the line that passes through C and is parallel to the vector AB. (b) Prove that for all vectors v and w in R", ||2v + w|24|v||2+ ||w||2 +4(v. w). At each step in your proof, you should name or state the property of the dot product that you are using. (c) Now let v and w be vectors in R³ and suppose that |v|| 2, ||w|| = 5 and ||2v + w|| = 7. (i) Use the result of part (b) to compute v w. (ii) Use the value of v w you found in part (c)(i) to compute ||vxw|. Give your answer as an exact value.