Answer :

Given three points A(2, 3, 5), B(3, 5, 8) and C(2, 7, 8) forming a triangle.

Let position vectors of the vertices A, B and C of ΔABC be, and respectively.

We know position vector of a point (x, y, z) is given by, where, and are unit vectors along X, Y and Z directions.

Similarly, we have and

To find area of ΔABC, we need to find at least two sides of the triangle. So, we will find vectors and.

Recall the vector is given by

Similarly, the vector is given by

Recall the area of the triangle whose adjacent sides are given by the two vectors and is where

Here, we have (a1, a2, a3) = (1, 2, 3) and (b1, b2, b3) = (0, 4, 3)

Recall the magnitude of the vector is

Now, we find.

Thus, area of the triangle is square units.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses

Find the angle beMathematics - Board Papers

If two vectors <sMathematics - Board Papers

If <span lang="ENMathematics - Exemplar

Show that area ofMathematics - Exemplar

Find the equationMathematics - Board Papers

Using vectors, fiMathematics - Board Papers

Find the angle beMathematics - Board Papers

Find the positionMathematics - Board Papers

<span lang="EN-USMathematics - Board Papers

If vectors <span Mathematics - Board Papers