Author Topic: Few questions (Read 534 times) Tweet Share

kettles · « **on:** August 03, 2012, 07:25:53 pm »

Hey guys i have a new batch of questions that im finding difficult to do.

http://imgur.com/zVdhF

2a was fine, but im finding it difficult to do b

Lasercookie · « **Reply #1 on:** August 03, 2012, 07:41:46 pm »

Use the dot product.

$\underset{\widetilde{}}{r_1}.\underset{\widetilde{}}{r_2} = |\underset{\widetilde{}}{r_1}||\underset{\widetilde{}}{r_2}|\cos \theta = x_1x_2 + y_1y_2 + z_1z_2$

Rearrange: $\cos \theta = \frac{x_1x_2 + y_1y_2 + z_1z_2}{|\underset{\widetilde{}}{r_1}||\underset{\widetilde{}}{r_2}|}$

Note that there are three dimensions.

Using the axis given in the diagram, as an (x,y,z) coordinate, $\underset{\widetilde{}}{r_1} = (3,-4,0) = 3\underset{\widetilde{}}{i} - 4\underset{\widetilde{}}{j} + 0\underset{\widetilde{}}{k}$ and $\underset{\widetilde{}}{r_2} = (2,6,-3) = 2\underset{\widetilde{}}{i} + 6\underset{\widetilde{}}{j} - 3\underset{\widetilde{}}{k}$ . You might want to state both vectors in a form you're more familiar with, e.g. i-j-k. Calculate the magnitudes too.

Evaluate:
$\cos \theta = \frac{(3 \cdot 2) + (-4 \cdot 6) + (0 \cdot -3)}{5\cdot7} = \frac{6 - 24}{35} = \frac{-18}{35}$

edit: my bad, I read the axis a bit wrong, let me fix that
edit: should be fixed now

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Author Topic: Few questions (Read 534 times) Tweet Share

kettles

Few questions

Lasercookie

Re: Vector diagram

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