1 year ago

Show that the three points whose position vectors are 7j+ 10k,-i + 6j+6k and - 4i + +9j + 6k form an isosceles right

Mathematics

1 answer:

Novay_Z [31]1 year ago

3 0

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 = $\sqrt{1+1+16} = \sqrt{18}$

BC = OC-OB = -4i+9j+6k-(-I+6j+6k) = -3i+3j

BC= $\sqrt{9+9} =\sqrt{18}$

CA = OA-OC = 7j+10k - (- 4i + +9j + 6k ) = 4i-2j+4k

CA = $\sqrt{16+4+16} =\sqrt{36} =4$

Since AB²+BC² = CA²

And AB=BC

Therefore it follows that ΔABC is a right angled isosceles triangle

You might be interested in

z+w−3 6z−10w =k =8 consider the system of equations above, where kkk is a constant. for which value of kkk are there i

Reptile [31]

Our system is the following :
$z+w-3=k\\
6z-10w=k,\\\text{Solve the first equation for z like this:} \\z=k-w+3\\\text{Substitute in the second equation like this:}\\6(k-w+3)-10w=k\\6k-16w+18=k\\16w=6k+18-k\\w=\frac{1}{16}(6k+18-k)$

As you see, the system has only one solution whenever the value of k is. Unlike you have not well written the system.

8 0

1 year ago

How do you simplify 77.28/9.2

Alinara [238K]

The answer is 8.4 all you do is divide them together to get your answer.

4 0

2 years ago

Polygon ABCD goes through a sequence of rigid transformations to form polygon A′B′C′D′. The sequence of transformations involved

spin [16.1K]

Refer to the diagram below

The shape ABCD first is reflected on the mirror line y = x

Then it is reflected again on the y-axis [equation of the line is x = 0]

4 0

2 years ago

Read 2 more answers

According to the Rational Root Theorem, the following are potential roots of f(x) = 6x4 + 5x3 – 33x2 – 12x + 20. -5/2,-2, 1, 10/

stiks02 [169]

-5/2 is the answer. I just took the test and got it right.

8 0

2 years ago

Read 2 more answers

Several friends each had 2/5 of a bag of peanuts left over from the baseball game. they realised that they could have bought 2 f

Reika [66]

Leftover per friend times number of friends=total left over
2/5 times number of friends=2
times both sides by 5/2
number of friends=10/2
number of friends=5

5 friends

6 0

2 years ago

Read 2 more answers