Home
Class 12
MATHS
Show that the points A(2 hat i- hat j+ ...

Show that the points `A(2 hat i- hat j+ hat k), B( hat i-3 hat j-5 hat k), C(3 hat i-4 hat j-4 hat k)`are the vertices of a right angled triangle.

Text Solution

AI Generated Solution

To show that the points \( A(2\hat{i} - \hat{j} + \hat{k}), B(\hat{i} - 3\hat{j} - 5\hat{k}), C(3\hat{i} - 4\hat{j} - 4\hat{k}) \) are the vertices of a right-angled triangle, we will follow these steps: ### Step 1: Find the position vectors of points A, B, and C The position vectors of the points are: - \( \vec{A} = 2\hat{i} - \hat{j} + \hat{k} \) - \( \vec{B} = \hat{i} - 3\hat{j} - 5\hat{k} \) - \( \vec{C} = 3\hat{i} - 4\hat{j} - 4\hat{k} \) ...
Promotional Banner

Topper's Solved these Questions

  • VECTOR ALGEBRA

    NCERT ENGLISH|Exercise Exercise 10.4|10 Videos

  • VECTOR ALGEBRA

    NCERT ENGLISH|Exercise EXERCISE 10.2|19 Videos

  • THREE DIMENSIONAL GEOMETRY

    NCERT ENGLISH|Exercise EXERCISE 11.3|14 Videos

Similar Questions

Explore conceptually related problems

Show that the vectors 2 hat i- hat j+ hat k , hat i-3 hat j-5 hat k and 3 hat i-4 hat j-4 hat k form the vertices of a right angled triangle.

Show that the vector 2 hat i- hat j+ hat k ,\ hat i-3 hat j-5 hat k ,\ 3 hat i-4 hat j-4 hat k form the sides of a rights angled triangle.

Prove that the points hat i- hat j ,4 hat i-3 hat j+ hat k and 2 hat i-4 hat j+5 hat k are the vertices of a right angled triangle.

Prove that the points hat i- hat j ,4 hat i-3 hat j+ hat k and 2 hat i-4 hat j+5 hat k are the vertices of a right angled triangle.

Show that the points A, B, C with position vectors 2 hat i- hat j+ hat k ,\ hat i-3 hat j-5 hat k and 3 hat i-4 hat j-4 hat k respectively, are the vertices of a right angled triangle. Also, find the remaining angles of the triangle.

Show that the points A(-2 hat i+3 hat j+5 hat k), B( hat i+2 hat j+3 hat k) and C(7 hat i- hat k) are collinear.

Show that the vectors vec a=3 hat i-2 hat j+ hat k , vec b= hat i+3 hat j+5 hat k , vec c=2 hat i+ hat j-4 hat k form a right angled triangle.

Show that the vectors vec a=3 hat i-2 hat j+ hat k ,\ vec b= hat i-3 hat j+5 hat k ,\ vec c=2 hat i+ hat j-4 hat k form a right angled triangle.

Show that the points A, B and C with position vectors, veca=3 hat i-4 hat j-4 hat k , vecb=2 hat i- hat j+ hat k and vecc= hat i-3 hat j-5 hat k respectively form the vertices of a right angled triangle.

Show that the points A ,\ B\ a n d\ C with position vectos vec a=3 hat i-4 hat j-4 hat k ,\ vec b=2 hat i- hat j+ hat k\ a n d\ vec c= hat i-3 hat j-5 hat k represent, form the vertices of a right angled triangle.