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In a two dimensional motion of a particl...

In a two dimensional motion of a particle, the particle moves from point A, with position vector `vec(r )_(1)` to point B, with position vector `vec(r )_(2)`. If the magnitudes of these vectors are, respectively, `r_(1 )=3` and `r_(2)=4` and the angles they make with the x-axis are `theta_(1)=75^(@)` and `theta_(2)=15^(@)`, respectively, then find the magnitude of the displacement vector.

A

`sqrt(3)`

B

`sqrt(13)`

C

`sqrt(5)`

D

`sqrt(1)`

Text Solution

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The correct Answer is:
B
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In a two diamensional motion of a particle, the particle moves from point A, with position vector vec(r )_(1) to point B, with position vector vec(r )_(2) . If the magnitudes of these vectors are, respectively, vec(r )=3 and r_(2)=4 and the angles they make with the x-axis are theta_(1)=75^(@) and theta_(2)=15^(@) , respectively, then find the magnitude of the displacement vector.

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Knowledge Check

  • The position vector of the point which divides the line segment joining the points with position vectors 2 vec(a) = 3b and vec(a) + vec(b) in the ratio 3:1 is

    A
    `(3 vec(a) - 2 vec(b))/(4)`
    B
    `( 7 vec(a) - 8 vec(b))/(4)`
    C
    `(3 vec(a))/( 4)`
    D
    `(5 vec(a))/( 4)`

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