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The x and y components of a position vec...

The x and y components of a position vector P have numerical values 5 and 6 respectively. Direction and magnitude of vector P are

A

`tan^(-1) ((6)/(5))` and `sqrt(61)`

B

`tan^(-1) ((5)/(6))` and `sqrt(61)`

C

`60^(@)` and 8

D

`30^(@)` and 9

Text Solution

Verified by Experts

The correct Answer is:
A
Let P be as shown in the figure, then according to the given information
`P_(x) = 5, P_(y) = 6`
`:. |P| = sqrt(P_(x)^(2) +P_(y)^(2)) = sqrt(25+36)`
`rArr |P| = sqrt(61)`
And `tan theta = (P_(y))/(P_(x)) = (6)/(5) rArr theta = tan^(-1) ((6)/(5))`
Thus, P having magnitude `sqrt(61)` lies in XY-plane at an angle `tan^(-1) ((6)/(5))` to the x-axis.
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Knowledge Check

  • The x and y components of vectors vec(A) are 4 m and 6 m respectively. The x and y components of vector (vec(A) +vec(B)) are 12 m and 10 m respectively. Then what are the x and y component . of vector vec(B) ?

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    A
    10
    B
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    D
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  • The component of a vector vecA along y-axis will have maximum value if

    A
    `vecA` makes an angle of 30° with y-axis
    B
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    C
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    D
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