If a-2-3-4k- find its components in yz plane

Compute the required valueGiven vector is a=2î 3ĵ+4k̂We know that, for a vector a=a_xî+a_yĵ+a_zk̂, the components in yz plane is √((a_y^2+a_z^2))Here,a_x=2, a_y ...

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Byju's Answer

Standard X

Mathematics

Thales Theorem

If a=2î-3ĵ+4k...

Question

If $\vec{a} = 2 \hat{i} - 3 \hat{j} + 4 \hat{k}$ , find its components in $y z$ plane

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Solution

Compute the required value
Given vector is $\vec{a} = 2 \hat{i} - 3 \hat{j} + 4 \hat{k}$
We know that, for a vector $\vec{a} = a_{x} \hat{i} + a_{y} \hat{j} + a_{z} \hat{k}$ , the components in $y z$ plane is $\sqrt{({a_{y}}^{2} + {a_{z}}^{2})}$
Here, $a_{x} = 2, a_{y} = - 3, a_{z} = 4$
Components in $y z$ plane $= \sqrt{({a_{y}}^{2} + {a_{z}}^{2})}$
$= \sqrt{{(- 3)}^{2} + {(4)}^{2}} = \sqrt{9 + 16} = \sqrt{25} = 5 u n i t s$
Hence the components in $y z$ plane is $5 u n i t s$

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