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High School Math Calculus Precalculus with Limits: A Graphing Approach

To check: The triangle formed be the vertices ( 1 , 2 , 0 ) , ( 0 , 0 , 0 ) and ( − 2 , 1 , 0 ) is an acute triangle, an obtuse triangle or a right triangle.

To check: The triangle formed be the vertices ( 1 , 2 , 0 ) , ( 0 , 0 , 0 ) and ( − 2 , 1 , 0 ) is an acute triangle, an obtuse triangle or a right triangle.

Precalculus with Limits: A Graphing Approach

Precalculus with Limits: A Graphing Approach

7th Edition

ISBN: 9781305071711

Author: Ron Larson

Publisher: Brooks/Cole

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Question

Chapter 10.2, Problem 61E

To determine

To check: The triangle formed be the vertices (1,2,0) , (0,0,0) and (−2,1,0) is an acute triangle, an obtuse triangle or a right triangle.

Expert Solution & Answer

Answer to Problem 61E

The triangle formed by joining the vertices (1,2,0) , (0,0,0) and (−2,1,0) is a right triangle.

Explanation of Solution

Given information:

The vertices of the triangle are (1,2,0) , (0,0,0) and (−2,1,0) .

Calculation:

Let the points be A(1,2,0) , B(0,0,0) and C(−2,1,0) be the vertices of the triangle.

The component form of the vector AB is 〈0−1,0−2,0−0〉=〈−1,−2,0〉 .

The component form of the vector BC is 〈−2−0,1−0,0−0〉=〈−2,1,0〉 .

The component form of the vector AC is 〈−2−1,1−2,0−0〉=〈−3,−1,0〉 .

Calculate the magnitude of the vector AB .

‖AB‖=(−1)2+(−2)2+(0)2=1+4+0=5

Calculate the magnitude of the vector BC .

‖BC‖=(−2)2+(1)2+(0)2=4+1+0=5

Calculate the magnitude of the vector AC .

‖AC‖=(−3)2+(−1)2+(0)2=9+1+0=10

Use the formula for angle between two vectors XY and YZ .

cosθ=XY.YZ‖XY‖‖YZ‖

Calculate the angle between the vectors AB and BC .

cosθ=AB⋅BC‖AB‖‖BC‖=〈−1,−2,0〉⋅〈−2,1,0〉5×5=−1×(−2)+(−2)×1+0×05=2−25=0

The solution for the equation cosθ=0 is AB θ=90° . So, the angle between the vectors and BC is 90° .

Therefore, the triangle formed by joining the vertices (1,2,0) , (0,0,0) and (−2,1,0) is a right triangle.

Chapter 10.2, Problem 60E

Chapter 10.2, Problem 62E

Chapter 10 Solutions

Precalculus with Limits: A Graphing Approach

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