a) A triangle ABC has vertices given by A(1,1,8), B(4,-3,-4) and C(-3,1,5)

(i) Determine the distance between B and C (in units).

(ii) Find the angle formed at the vertex A (2 decimal places)

Please help...

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- Aug 19th 2007, 05:54 PMUnt0tVertices help
a) A triangle ABC has vertices given by A(1,1,8), B(4,-3,-4) and C(-3,1,5)

(i) Determine the distance between B and C (in units).

(ii) Find the angle formed at the vertex A (2 decimal places)

Please help... - Aug 19th 2007, 07:03 PMSoroban
Hello, Unt0t!

Quote:

A triangle ABC has vertices given by A(1,1,8), B(4,-3,-4) and C(-3,1,5)

(a) Determine the distance between B and C (in units).

Quote:

(b) Find the angle formed at the vertex A (2 decimal places)

Let:

Let:

Then: .

. . . . . . . .

Therefore: .

- Aug 19th 2007, 07:36 PMUnt0t
Thanks, i've got another question now.

Let u = (1, -3, -1), v = (1, 1, 2), w = (-2, -2, 1), x = (-1, -1, 1).

a) By considering the dot product only, identify 2 vectors that will satisfy each of the following situations:

(i) the angle between them is less than (pie)/2;

(ii) the angle between them is greater than (pie)/2;

Justify your answers by considering the relationship between the dot product and the cosine of the angle.

b) Identify 2 vectors that will be perpendicular to each other. Justify your answer. - Aug 19th 2007, 10:28 PMred_dog
If and then

We have

.

Now, using these, you can solve the problem.