Show that the three points whose position vectors are 7j+ 10k,-i + 6j+6k and - 4i + +9j + 6k form an isosceles right
1 answer:
Answer:
AB = √18 , BC=√18 and CA =4
AB²+BC² = CA² and AB=BC
ΔABC isosceles right angled triangle.
Step-by-step explanation:
Given vectors are 7j+ 10k,-i + 6j+6k and - 4i + +9j + 6k
A( 0,7,10), B( -1,6,6) C(-4,9,6)
AB⁻ = OB-OA = -I+6j+6k-(7j+10k) = -I-j-4k
AB =
BC = OC-OB = -4i+9j+6k-(-I+6j+6k) = -3i+3j
BC=
CA = OA-OC = 7j+10k - (- 4i + +9j + 6k ) = 4i-2j+4k
CA =
Since AB²+BC² = CA²
And AB=BC
Therefore it follows that ΔABC is a right angled isosceles triangle
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By using distance formula :
Given points = ( 3 , 5.25 ) and ( 3 , - 8.75 )
On applying formula, we get
Hence, Option D is correct.
Given points = ( 3 , 5.25 ) and ( 3 , - 8.75 )
On applying formula, we get
Hence, Option D is correct.
Answer:
The length of the fence needed to surround this garden is 188 meters.
Step-by-step explanation:
Given : A fence is guarding off a vegetable garden in the form of a rectangle. It has one side that is 10 m greater than the other side.
To find : The length of the fence needed to surround this garden if the area of the vegetable garden is 2184 m² ?
Solution :
Let the one side of rectangle be 'x'.
Then the other side is 'x+10'.
The area of the rectangle is 2184 m²,
i.e.
Solve by middle term split,
Reject negative value,
The side of the rectangle is 42 m.
The other side is 42+10=52 m
The perimeter of the rectangle is
Therefore, the length of the fence needed to surround this garden is 188 meter.