Only A and B on the line segment AB such that C divides ABin the ratio 3:2 and let point D lie on the linesegment OA such that D divides OA in theratio 5: 2. Denote by P the intersection pointbetween line segments OC and BD. Find theratio in which P divides OC and BD.3. Let A(-3, 2, 1), В(3, —3, 1) and C(5, A, 2)denote three vertices of parallelogram DABCD.(a) Find coordinates of the vertex D.(b) Calculate parameter A so that|AD| = /14.(c) Use part (b) and for the bigger value of Acheck is the set (AD BD. AC} linearlyindependent. If the set {AB BD AC) islinearly dependent, write the vector AC.a linear combination of vectors AD andBD.as

In a parallelogram , diagonals bisect each other.

Answered: 3. Let A(-3,2, X), B(3, –3, 1) and C(5,…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter1: Vectors

Section1.2: Length And Angle: The Dot Product

Problem 6AEXP

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The following problem is based on this theorem: A median of a triangle separates it into two triangles of equal area. In the figure, RST has median RV. a Explain why ARSV=ARVT. b If ARST=40.8cm2, find ARSV.
What is the limit of mRTS if T lies in the interior of the shaded region?
Three holes are bored in a checking gage. The lower left edge of the gage is the reference point for the hole locations. Sketch the hole locations and determine the missing distances. From the reference point: Hole #1 is 1332 to the right, and 158up. Hole #2 is 2164 to the right, and 2316up. Hole #3 is 314to the right, and 312up. Determine: a. The horizontal distance between hole #1 and hole #2. b. The horizontal distance between hole #2 and hole #3. c. The horizontal distance between hole #1 and hole #3. d. The vertical distance between hole #1 and hole #2. e. The vertical distance between hole #2 and hole #3. f. The vertical distance between hole #1 and hole #3.
For exercises 34 and 35, EFis the median of trapezoid ABCD in the figure above. Suppose that EM=7.1andMF=3.5 Find: a AB b EF c DC d Whether EF=12(AB+DC)
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Use Exercise 33 and the following drawing to complete the proof of this theorem: The length of the median of a trapezoid is one-half the sum of the lengths of the two bases. Given: Trapezoid ABCD with median MN Prove: MN=12(AB+CD) 33. Use Theorem 5.6.1 and the drawing to complete the proof of this theorem: If a line is parallel to one side of a triangle and passes through the midpoint of a second side, then it will pass through the midpoint of the third side. Given: RST with M the midpoint of RS;MNST Prove: N is the midpoint of RT
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The point mid ay between (a, b) and (c, d) _____________. So the point midway between (1, 2) and (7, 10) is ___________.
Use Theorem 5.6.3 to complete the proof of this theorem: If the bisector of an angle of a triangle also bisects the opposite side, then the triangle is an isosceles triangle. Given: XYZ;YW bisects XYZ;WXWZ Prove: XYZ is isosceles HINT: Use a proportion to show that YX=YZ.
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3. Let A(-3,2, X), B(3, –3, 1) and C(5, X, 2) denote three vertices of parallelogram DABCD. (a) Find coordinates of the vertex D. (b) Calculate parameter A so that |AD| = V14. SO