The sum of the lengths of the projections of 2 i ^ + 3 j ^ + 4 k ^ on the coordinate axes is

Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Mathematics3D Coordinate GeometryCoordinates of a point in space, Direction cosines,Easy2 minPYQ_2026

MathematicsEasysingle choice

The sum of the lengths of the projections of $2 \hat{i} + 3 \hat{j} + 4 \hat{k}$ on the coordinate axes is

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Solution:

Let the given vector be $v = 2 \hat{i} + 3 \hat{j} + 4 \hat{k}$ .

The lengths of the projections of a vector on the coordinate axes are the absolute values of its scalar components along the respective axes.

Length of projection on the x-axis = $∣2∣ = 2$

Length of projection on the y-axis = $∣3∣ = 3$

Length of projection on the z-axis = $∣4∣ = 4$

The sum of the lengths of these projections is $2 + 3 + 4 = 9$ .

Answer: $9$

Stream:MHT_CETSubject:MathematicsTopic:3D Coordinate GeometrySubtopic:Coordinates of a point in space, Direction cosines,

⏱ 2mℹ️ Source: PYQ_2026

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