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Question

The projection of a line segment having length 13 cm on xy,yz planes are 5,410 respectively. The projection of a line segment on xz plane is

A
133
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B
153
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C
33
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D
121
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Solution

The correct option is A 133
Let the line segment be x^i+y^j+z^k.
Its length is 13 cm

=(x0)2+(y0)2+(z0)2=13x2+y2+z2=169 (1)

Its projection of xy plane is 5
As z - coordinates is zero on xy plane,
x2+y2=5x2+y2=25 (2)

Similarly on yz plane,
Y2+z2=410y2+z2=160 (3)

Putting (3) in (1), we get,
x2+160=169x2=9x=3

Putting x value in (2), we get,
9+y2=25
y=4

Putting y value in (3), we get,
16+z2=160
z=12

Therefore, projection of xz plane is x2+x2
=32+122
=153

Hence the answer is 153

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