vector multiplication

**winterwyrm** · September 9th 2008, 07:11 PM

Two vectors are given by a = 9.1i + 1.1j and b = 4.9i + 3.8j. Find (a)|a × b|, (b)a · b, (c)(a + b) · b, and (d) the component of a along the direction of b?

**o_O** · September 9th 2008, 07:35 PM

What exactly are you having trouble with?

(a) The cross product is only defined for 3-dimensional Euclidean space. So unless you assume the unit vector k to be 0, you can't perform this operation.

(b) $\bold{a} \cdot \bold{b} = a_{1}b_{1} + a_{2}b_{2}$ . Just plug it in.

(c) $\bold{a} + \bold{b} = (a_{1} + b_{1}) \bold{i} + (a_{2} + b_{2}) \bold{j}$

(d) The orthogonal projection of a along b is given by: $\text{proj}_{\bold{b}}\bold{a} = \frac{\bold{a} \cdot \bold{b}}{\mid \bold{b} \mid ^2} \ \bold{b}$

**winterwyrm** · September 9th 2008, 08:32 PM

k isn't, but I think I figured it out, since there is no z term, a ton of terms in this one equation cancel out, sorry about that. Thanks for your help on the other three parts though =]

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