(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

It is given that the soltuion of the vector equation y x a=b is

[tex]\underline{y}= \lambda \underline{a} + \frac{\underline{a} \times \underline{b}}{| \underline{a}|^2}[/tex]

with a . b=0 and [itex]\lambda[/itex] is a scalar. Use this information to find the solution of the equation (x x a) + (x . b)c=d.

Where x is the unknown vector and [itex]\underline{a} \cdot \underline{c} \neq 0[/tex]

2. Relevant equations

[tex]\underline{A} \cdot \underline{B}= |\underline{A}| |\underline{B}|cos\theta[/tex]

[tex]\underline{A} \times \underline{B} = |\underline{A}| |\underline{B}|sin\theta \hat{n}[/tex]

3. The attempt at a solution

This is my method of thinking.

If [itex]\underline{a} \cdot \underline{b} =0 [/itex] then this means that a and b are perpendicular

[tex]y \times a =b[/tex]

[tex]a \time (y \times a)= a \times b[/tex]

[tex]= y(a \cdot c)-a(a \cdot y)= a \times b[/tex]

[tex]\Rightarrow = y(a \cdot c)=a(a \cdot y)+a \times b[/tex]

[tex]\div a \cdot c[/tex]

[tex]y= a \frac{a \cdot y}{a \cdot c} + \frac{a \times b}{a \cdot c}[/tex]

Comparing this with the given solution:

[tex]\lambda = \frac{a \cdot y}{a \cdot c}[/tex]

AND

[tex]|a|^2={a \cdot c}[/tex]

On the right track so far?

[tex](x \times a) + (x \cdot b)c=d[/tex]

[tex]a \times (x \times a)+ a \times (x \cdot b)c= a \times d[/tex]

[tex] x(a \cdot a)+ a \times c(x \cdot b)=a \times d[/tex]

[tex]x |a|^2 + a \times c(x \cdot b)= a \times d[/tex]

[tex]x(a \cdot c) + a \times c( x \cdot b)= a \times d[/tex]

and I am stuck here.

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# Homework Help: How do I begin to solve this vector/cross product problem?

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