Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
The three vertices of a triangle are at A (7,-1,3), B (-3,3,-4) and C(-3,1, 5). Find: (use Dot product) a. The vector projection of RAB on RAC b. The length of the perimeter of the triangle

The three vertices of a triangle are at A (7,-1,3), B (-3,3,-4) and C(-3,1, 5). Find: (use Dot product) a. The vector projection of RAB on RAC b. The length of the perimeter of the triangle

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter2: Parallel Lines
Section2.4: The Angles Of A Triangle
Problem 23E: Consider any triangle and one exterior angle at each vertex. What is the sum of the measures of the...
See similar textbooks
icon
Related questions
Question

Please answer and write correctly and neatly.

The three vertices of a triangle are at A (7,-1,3), B (-3,3,-4) and C(-3,1, 5). Find: (use Dot product)

a. The vector projection of RAB on RAC
b. The length of the perimeter of the triangle

The three vertices of a triangle are at A(7 To find: (a) RAB (b) RAC (c) The angle BAC Step3 c) lution: ) The vertices of the triangle A=(7, — 1, 3)= 7i − j + 3k B=(-3, 3, 4)= −3i + 3j − 4k C=(−3, 1, 5)= −3i+j+5k Step4 d) Where, i, j, and k are the u Since, the vector RAB is give RAB=B - A =(−3i + 3j - 4k)−(7i − j + 3k) =-3i + 3j - 4k - 7i+j - 3k =-10i + 4j - 7k herefore, RAB=-10i +4j - 7k Since, A=7i- j + 3k C=-3i+j+ 5k The vector RAC is given by RAC CA =(-3i+j+5k)-(7i- j + 3k) =-3i+j+ 5k - 7i+j - 3k =-10i + 2j + 2k herefore, RAC=-10i +2j + 2k
Transcribed Image Text:The three vertices of a triangle are at A(7 To find: (a) RAB (b) RAC (c) The angle BAC Step3 c) lution: ) The vertices of the triangle A=(7, — 1, 3)= 7i − j + 3k B=(-3, 3, 4)= −3i + 3j − 4k C=(−3, 1, 5)= −3i+j+5k Step4 d) Where, i, j, and k are the u Since, the vector RAB is give RAB=B - A =(−3i + 3j - 4k)−(7i − j + 3k) =-3i + 3j - 4k - 7i+j - 3k =-10i + 4j - 7k herefore, RAB=-10i +4j - 7k Since, A=7i- j + 3k C=-3i+j+ 5k The vector RAC is given by RAC CA =(-3i+j+5k)-(7i- j + 3k) =-3i+j+ 5k - 7i+j - 3k =-10i + 2j + 2k herefore, RAC=-10i +2j + 2k
Since, RAB=-10i + 4j - 7k RAC -10i + 2j + 2k RAB RAC (-10i + 4j – 7k).(-10i +2j+2 =(−10)(-10)+(4)(2)+(−7)(2) =100+ 8 - 14 =108 14 =94 ||RAB||= (−10)² +4² + (−7)² =√/100 + 16 + 49 =√/165 |Rac||=√(−10)² + 2² +2² 100+ 4 + 4 . - =√108 =6√3 Let, BAC is the angle betwee We know that the angle bet a.b से || || b || Therefore, the angle between 0=cos OBAC=COS g, RAB RAC=94, ||RAB||= √165, and ||RAC|| BAC COS RAB RAC || RAB || ||RAC || ( 94 (√165) (6√3) calculator we get Using OBAC 45. 23793134° erefore, BAC-45. 23793134°
Transcribed Image Text:Since, RAB=-10i + 4j - 7k RAC -10i + 2j + 2k RAB RAC (-10i + 4j – 7k).(-10i +2j+2 =(−10)(-10)+(4)(2)+(−7)(2) =100+ 8 - 14 =108 14 =94 ||RAB||= (−10)² +4² + (−7)² =√/100 + 16 + 49 =√/165 |Rac||=√(−10)² + 2² +2² 100+ 4 + 4 . - =√108 =6√3 Let, BAC is the angle betwee We know that the angle bet a.b से || || b || Therefore, the angle between 0=cos OBAC=COS g, RAB RAC=94, ||RAB||= √165, and ||RAC|| BAC COS RAB RAC || RAB || ||RAC || ( 94 (√165) (6√3) calculator we get Using OBAC 45. 23793134° erefore, BAC-45. 23793134°
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition…
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
SEE MORE TEXTBOOKS