(a) Draw the vectors a=[3, 2], b=[2,-1], and c=[7, 1]. (b) Show, by means of a sketch, that there are scalars s and t such that
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Answer:
The three given points are the vertices of a right triangle.
Step-by-step explanation:
To determine that the three points are the vertices of a right triangle let us find the distance between each two points
The formula of the distance is
∵ = 6 and
= -6
∵ = 9 and
= -6
∴ =
∴ = 3
∵ = 6 and
= -6
∵ = 9 and
= 1
∴ =
∴ =
∵ = 9 and
= 1
∵ = 9 and
= -6
∴ =
∴ = 7
<em>Let us use the fact that if the square of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle at the vertex which opposite to the longest side</em>
∵ The longest side is
∵ The other two sides are 3 and 7
∵ ( )² = 58
∵ (3)² + (7)² = 9 + 49 = 58
∴ ( )² = (3)² + (7)²
- By using the fact above
∴ The triangle is a right triangle
The three given points are the vertices of a right triangle.