First slide

Motion in a plane

Question

If $\large \vec A=2\hat i-3\hat j+4\hat k$ its components in yz plane and zx plane are respectively

Moderate

A

√13 and 5
B

5 and 2√5
C

2√5 and √13
D

√13 and √29

Solution

$\large \overline A = 2\widehat i - 3\widehat j + 4\widehat k = {A_x}\widehat i + {A_y}\widehat j + {A_z}\widehat k$
→ In yz plane = $\large \sqrt {A_y^2 + A_z^2} = \sqrt {{{( - 3)}^2} + {4^2}}$ $\large = \sqrt {9 + 16} = 5units$
→ In zx plane = $\large \sqrt {A_z^2 + A_x^2} = \sqrt {16 + 4} = 2\sqrt 5 units$
$\large \therefore$ 5 and 2√5

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