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April 14th, 2017, 07:19 AM   #1
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vector

find the modulus of vector V.
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April 14th, 2017, 07:45 AM   #2
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$2\vec{V} + \vec{V} \times (\hat{i}+2\hat{j}) = 2\hat{i}+\hat{k}$

let $\vec{V} = a\hat{i} + b\hat{j} + c\hat{k}$

$\vec{V} \times (\hat{i}+2\hat{j})=\begin{vmatrix}
i & j & k\\
a & b & c\\
1 & 2 & 0
\end{vmatrix} = (-2c)-(c)+(2a-b)=2a\hat{i}-b\hat{j}-3c\hat{k}$

$2(a\hat{i} + b\hat{j} + c\hat{k}) + (2a\hat{i}-b\hat{j}-3c\hat{k}) = 2\hat{i}+\hat{k}$

can you finish ?
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April 14th, 2017, 08:38 AM   #3
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Yeah. thankyou!
it can be done by assuming it. But is there any way to find it without assuming it as ai+bj+ck.
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April 14th, 2017, 08:56 AM   #4
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You have two other vectors in the equation given in component form. I used $a,b, \text{ and } c$ as constant multiples of the unit vectors for V in each direction to express V in component form also. You understand you have to solve for the constants $a,b, \text{ and } c$, correct?

... how else would you do it?
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Last edited by skeeter; April 14th, 2017 at 09:32 AM.
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April 15th, 2017, 03:44 AM   #5
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okay. yeah
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