if the position vectors of the vertices of a triangle ABC are OA=3i+j+2k,OB=i+2j+3k and OC=2i+3j+k, then the length of the altitude of triangle ABC drawn from A is
Answers
Answer:
Can u sent photo this question
Step-by-step explanation:
Let us solve the problem using three dimension coordinates system.
From the given information, we can write the vertices of ABC to be A (3, 1, 2), B (1, 2, 3) and C (2, 3, 1).
Here AB = √{(3 - 1)² + (1 - 2)² + (2 - 3)²} = √6,
BC = √{(1 - 2)² + (2 - 3)² + (3 - 1)²} = √6
and CA = √{(2 - 3)² + (3 - 1)² + (1 - 2)² } = √6.
Since ABC is an equilateral triangle, the altitude drawn from A touches the base BC in its middle point, which if assumed to be D, then the coordinates of D are
( (1 + 2)/2, (2 + 3)/2, (3 + 1)/2 )
i.e., (3/2, 5/2, 2)
Therefore the distance of A from D
= √{(3 - 3/2)² + (1 - 5/2)² + (2 - 2)²} units
= √(9/4 + 9/4) units
= √(18/4) units
= 3/2 × √2 units
Answer:
The length of the altitude of triangle ABC drawn from A is 3/2 × √2 units.
Read more on Brainly.in
A right rectangular prism has these dimensions: Length: 1 1/2 units Width: 1/2 unit Height: 3/4 unit How many cubes ...
- https://brainly.in/question/12304803