physics vectors

Question

If A = i + 5j - k and B = -3i - 2j + 5k. Answer the following problems.

2A + B

A – 2B

A • B

A X B

Answer 1

The first two, just do what it says and add the i, j, and k terms separately:

I'll do the first one:

2A = 2(i +5j -k) = 2i + 10j - 2k

2A + B = (2-3)i +(10-2)j + (-2+5)k = -i + 8j +3k

3rd one is dot product = Summation of A_iB_i where A is A₁i + A₂j +A₃k Just multiply the terms for I, j, and k from the two vectors and add them.

4th one is the cross (or vector) product. The easiest way to do this is to write the following determinant and multiply it out.

| i j k|

| 1 5 -1|

|-3 -2 5|

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