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A (–4, –1, 2), B (3, –2, –1) and C (–1, 3, –4), AB= 7? −...

A (–4, –1, 2), B (3, –2, –1) and C (–1, 3, –4),

AB= 7? − ? − 3?

CB = 4? − 5? + 3?

AC = 3? + 5? - 2?

Question 7: Express the vector AC as the sum of two vectors: AC = ? + ?, where ? is parallel to the vector CB and ? is perpendicular to CB. Given that AC ∙ CB = −26 and that CB = √50, determine the y-component of the vector ?. [Please enter your answer correct to at least 2 decimal places.]

Question 8: Suppose that we wish to determine the equation for the plane through the point C and perpendicular to the vector AB. If the equation for this plane is expressed in the form ? + ?y+ cz + ? = 0 (that is, 1? + ?y + ?z + ? = 0), what is the value of b? [Please enter your answer correct to at least 3 decimal places.]
Question 9: Find the x component of the vector product ? = CB × AB.

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