Given the triangle ABC, let u= CA/2+ CB/3.(a) Explain why there is and is unique the point X on the line AB such that CX//u (Figure ). (b) Show that X belongs to segment AB and express CX as a function of CA, CB.Answer: Figure 2 Answer:a) The vector u is not parallel AB because, if it were, there would be a real number A suchthat CA/2+CB/3=NAB=N(AC+CB) = -ACA + ACB, and then - 1/2 = A = 1/3 which is impossible.Consequently, the line parallel to which contains C is not parallel to line AB. As these arecoplanar lines, we conclude that they are concurrent and that, therefore, the point X existsand is unique.b)CX =CÁ +СВ5 * CBAB18

Explanation for part a) is correct and sufficient. For unique point, two vectors intersect at a…

Given the triangle ABC, let u= CA/2+ CB/3. (a) Explain why there is and is unique the point X on the line AB such that CX//u (Figure ). (b) Show that X belongs to segment AB and express CX as a function of CA, CB. Answer: Figure 2

Given the triangle ABC, let u= CA/2+ CB/3. (a) Explain why there is and is unique the point X on the line AB such that CX//u (Figure ). (b) Show that X belongs to segment AB and express CX as a function of CA, CB. Answer: Figure 2

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.CT: Chapter Test

Problem 16CT: How many six-digit license plates can be made if no plate begins with 0 or 1?

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Question

Given the triangle ABC, let u= CA/2+ CB/3.

(a) Explain why there is and is unique the point X on the line AB such that CX//u (Figure ).

(b) Show that X belongs to segment AB and express CX as a function of CA, CB.

Answer: Figure 2

Answer:
a) The vector u is not parallel AB because, if it were, there would be a real number A such
that CA/2+CB/3=NAB=N(AC+CB) = -ACA + ACB, and then - 1/2 = A = 1/3 which is impossible.
Consequently, the line parallel to which contains C is not parallel to line AB. As these are
coplanar lines, we conclude that they are concurrent and that, therefore, the point X exists
and is unique.
b)
CX =
CÁ +
СВ
5

Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.

Expert Solution