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

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- Sep 9th 2008, 07:11 PMwinterwyrmvector multiplication
Two vectors are given by

*a*= 9.1*i*+ 1.1*j*and*b*= 4.9*i*+ 3.8*j*. Find**(a)**|*a*×*b*|,**(b)***a*·*b*,**(c)**(*a*+*b*) ·*b*, and**(d)**the component of*a*along the direction of*b*? - Sep 9th 2008, 07:35 PMo_O
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) $\displaystyle \bold{a} \cdot \bold{b} = a_{1}b_{1} + a_{2}b_{2}$. Just plug it in.

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

(d) The orthogonal projection of a along b is given by: $\displaystyle \text{proj}_{\bold{b}}\bold{a} = \frac{\bold{a} \cdot \bold{b}}{\mid \bold{b} \mid ^2} \ \bold{b}$ - Sep 9th 2008, 08:32 PMwinterwyrm
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 =]