If overline{a}=3 hat{i}-5 hat{j} and overline | vedclass

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(B) Given vectors are $\overline{a} = 3 \hat{i} - 5 \hat{j}$ and $\overline{b} = 6 \hat{i} - 3 \hat{j}$.The vector $\overline{c}$ is defined as the cr

Vedclass · Accepted Answer

$\sqrt{34}: \sqrt{45}: 39$

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(B) Given vectors are $\overline{a} = 3 \hat{i} - 5 \hat{j}$ and $\overline{b} = 6 \hat{i} - 3 \hat{j}$.The vector $\overline{c}$ is defined as the cross product of $\overline{a}$ and $\overline{b}$:$\overline{c} = \overline{a} 	imes \overline{b} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 3 & -5 & 0 \ 6 & -3 & 0 \end{vmatrix}$Calculating the determinant:$\overline{c} = \hat{i}(0 - 0) - \hat{j}(0 - 0) + \hat{k}(-9 - (-30)) = \hat{k}(-9 + 30) = 39 \hat{k}$.Now,we find the magnitudes of the vectors:$a = |\overline{a}| = \sqrt{3^2 + (-5)^2} = \sqrt{9 + 25} = \sqrt{34}$.$b = |\overline{b}| = \sqrt{6^2 + (-3)^2} = \sqrt{36 + 9} = \sqrt{45}$.$c = |\overline{c}| = |39 \hat{k}| = 39$.Therefore,the ratio $a: b: c = \sqrt{34}: \sqrt{45}: 39$.

If $\overline{a}=3 \hat{i}-5 \hat{j}$ and $\overline{b}=6 \hat{i}-3 \hat{j}$ are two vectors and $\overline{c}$ is a vector such that $\overline{c}=\overline{a} \times \overline{b}$,then the ratio $a: b: c$ is:

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