Question

Determine the perimeter of the triangle with vertices at A(1, -2, 1), B(0, 3, 2) and C(-2, -1, 3). Also, determine the midpoint of each side and the perimeter of the triangle formed by the midpoints. Find the unit vector in the direction of A and verify that it has length 1. a. A = ?2, 5? b. A = ??3, 2, 1/4?

          Determine the perimeter of the triangle with vertices at A(1, -2, 1), B(0, 3, 2) and C(-2, -1, 3). Also, determine the midpoint of each side and the perimeter of the triangle formed by the midpoints.

Find the unit vector in the direction of A and verify that it has length 1.

a. A = ?2, 5?
b. A = ??3, 2, 1/4?

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Determine the perimeter of the triangle with vertices at A(1, -2, 1), B(0, 3, 2) and C(-2, -1, 3). Also, determine the midpoint of each side and the perimeter of the triangle formed by the midpoints.

Find the unit vector in the direction of A and verify that it has length 1.

a. A = ?2, 5?
b. A = ??3, 2, 1/4?

Added by Josep T.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

05/25/2023

Step 1

We can use the distance formula for this: AB = sqrt((0-1)^2 + (3-(-2))^2 + (2-1)^2) = sqrt(1 + 25 + 1) = sqrt(27) BC = sqrt((-2-0)^2 + (-1-3)^2 + (3-2)^2) = sqrt(4 + 16 + 1) = sqrt(21) CA = sqrt((1-(-2))^2 + (-2-(-1))^2 + (1-3)^2) = sqrt(9 + 1 + 4) = Show more…

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Determine the perimeter of the triangle with vertices at A(1,-2,1), B(0,3,2), and C(-2,-1,3). Also, determine the midpoint of each side and the perimeter of the triangle formed by the midpoints. Find the unit vector in the direction of A and verify that it has length 1. a. A = ✐2, 5✑ b. A = ✐√3, 2, 1/4✑

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Transcript

00:01 Hi, in this question we have been given vertices of a triangle as a point has vertices of 1, minus 2, 1.

00:13 Then second vertex is having coordinate of 0, 3, 2 and c is minus 2, 1, minus 1 and then so first of all we need to find the midpoint of these vertices of triangle and then we will find the perimeter.

00:35 So here let us draw this triangle.

00:38 So this is let us consider a triangle.

00:42 Here we have b coordinate that is 0, 3, 2 and this is a, 1, minus 2, 1 and this is c which is having minus 2, minus 1 and 3.

00:56 So this point will be vertices of ec, this point will be vertices of av and this is midpoint of vertices ac.

01:07 Let us name this as p, q and r.

01:11 So midpoint is given by x1 plus x2 divided by 2, y1 plus y2 divided by and z1 plus z2 divided by 2.

01:29 So we will be using this formula to find the midpoint of each vertices.

01:34 So first of all we will calculate midpoint of av.

01:42 So this is p and its coordinate will be 0 plus 1 divided by 2, then 3 minus 2 divided by 2, then 2 plus 1 divided by 2.

01:56 So on solving this we will get the coordinate of p as 1 divided by 2, 1 divided by 2 and this is 3 divided by 2.

02:06 Similarly we will find the midpoint of bc.

02:15 So this is q and here we will have 0 minus 2 divided by 2, then 3 minus 1 divided by 2, then 2 plus 3 divided by 2.

02:29 So this is q and its coordinate will be now minus 1, 1 and 5 divided by 2.

02:36 So in similar way midpoint of ac that is r, coordinate will be minus 2 plus 1 divided by 2, then minus 1 minus 2 divided by 2, then it's 3 plus 1 divided by 2.

02:58 So this will be minus 1 divided by 2, then minus 3 divided by 2 and then 2.

03:05 So we have calculated the coordinate of p, q and r...

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