X-component of a- is twice of its Y-component- If the magnitude of the vector is 5-2 and it makes an angle of 135- with z-axis then the components of vector is

The correct option is B 2√(5),√(5), 5 a_x=2a_y, cosγ=a_z/a=cos 135^∘= 1/√(2) ⇒ a_z= a/√(2)= 5√(2)/√(2)= 5 Now a_x^2+a_y^2+a_z^2=50⇒ 4a^2_y+ ...

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Byju's Answer

Standard XII

Physics

Vector Component

X-component o...

Question

X-component of $\to a$ is twice of its Y-component. If the magnitude of the vector is $5 \sqrt{2}$ and it makes an angle of $135^{\circ}$ with z-axis then the components of vector is

2 \sqrt{3}, \sqrt{3}, - 3

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2 \sqrt{6}, \sqrt{6}, - 6

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2 \sqrt{5}, \sqrt{5}, - 5

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2 \sqrt{2}, \sqrt{2}, - 2

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Solution

The correct option is B $2 \sqrt{5}, \sqrt{5}, - 5$
$a_{x} = 2 a_{y}, c o s γ = \frac{a_{z}}{a} = c o s 135^{\circ} = - \frac{1}{\sqrt{2}}$
$\Rightarrow a_{z} = - \frac{a}{\sqrt{2}} = - \frac{5 \sqrt{2}}{\sqrt{2}} = - 5$
Now $a_{x}^{2} + a_{y}^{2} + a_{z}^{2} = 50 \Rightarrow 4 a_{y}^{2} + a_{y}^{2} + 25 = 50$
$\Rightarrow a_{y}^{2} = 5 \Rightarrow a_{y} = \pm \sqrt{5} \Rightarrow a_{x} = \pm 2 \sqrt{5}$

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X-component of →a is twice of its Y-component. If the magnitude of the vector is 5√2 and it makes an angle of 135∘ with z-axis then the components of vector is

The correct option is B 2√5,√5,−5ax=2ay,cosγ=aza=cos135∘=−1√2⇒az=−a√2=−5√2√2=−5Now a2x+a2y+a2z=50⇒4a2y+a2y+25=50⇒a2y=5⇒ay=±√5⇒ax=±2√5

X-component of $\to a$ is twice of its Y-component. If the magnitude of the vector is $5 \sqrt{2}$ and it makes an angle of $135^{\circ}$ with z-axis then the components of vector is