(C) Let the vertices be $O(0, 0)$,$A(\cos \alpha, \sin \alpha)$,and $B(-\sin \alpha, \cos \alpha)$.The square of the distance $OA$ is given by $OA^2 =

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(C) Let the vertices be $O(0, 0)$,$A(\cos \alpha, \sin \alpha)$,and $B(-\sin \alpha, \cos \alpha)$.The square of the distance $OA$ is given by $OA^2 = (\cos \alpha - 0)^2 + (\sin \alpha - 0)^2 = \cos^2 \alpha + \sin^2 \alpha = 1$.The square of the distance $OB$ is given by $OB^2 = (-\sin \alpha - 0)^2 + (\cos \alpha - 0)^2 = \sin^2 \alpha + \cos^2 \alpha = 1$.Therefore,$OA^2 + OB^2 = 1 + 1 = 2$.

Class 11 Mathematics Straight Line System of co-ordinates, Distance between two points, Section formulae

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If the coordinates of the vertices of $\Delta OAB$ are $(0, 0)$,$(\cos \alpha, \sin \alpha)$,and $(-\sin \alpha, \cos \alpha)$ respectively,then $OA^2 + OB^2 = $

A
$0$
B
$1$
C
$2$
D
$3$

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Straight Line

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System of co-ordinates, Distance between two points, Section formulae

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If the coordinates of the vertices of $\Delta OAB$ are $(0, 0)$,$(\cos \alpha, \sin \alpha)$,and $(-\sin \alpha, \cos \alpha)$ respectively,then $OA^2 + OB^2 = $

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The distance between the points $(7, 5)$ and $(3, 2)$ is equal to ........... $unit$.

What are the coordinates of the point that divides the line segment joining the points $(-3, -4)$ and $(-8, 7)$ externally in the ratio $7 : 5$?

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What are the coordinates of the points of trisection of the line segment joining the points $(-3, -3)$ and $(6, 6)$?

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