Question

The projection of a line segment on the coordinates axes are 2, 3, 6. Then the length of line segment is
A. 7
B. 5
C. 1
D. 11

Answer 1

Hint: Here we have given the projection on the coordinate axes. Firstly we have to find direction cosines that are calculated by dividing the vector length by the associated coordinate point provided. We are going to use the length of line segment formula to solve this question.

Formula Used:
Length of vector can be given as $=\sqrt{(a_1)^2+(a_2)^2+(a_3)^2}

Complete step-by-step solution:
Given: Projection line segment coordinates are 2, 3, 6
Let the position of line segment end point are \[\overrightarrow P \] AND \[\overrightarrow Q \]
Let $\hat i$ , $\hat j$ and $\hat k$ be the direction cosine.
Length of line segment$ = \sqrt {{{\left( x \right)}^2} + {{\left( y \right)}^2} + {{\left( z \right)}^2}} $
Therefore length of line segment by using the above formula
$\vec {PQ} = \sqrt {{{\left( 2 \right)}^2} + {{\left( 3 \right)}^2} + {{\left( 6 \right)}^2}} $
$\vec {PQ}= \sqrt {49} $
$\vec {PQ} = 7$
Hence the correct option is A (7).
So, option A is correct.

Additional Information:
The definition of "projection" in mathematics is "The representation of a figure or solid on a plane as it would look from a specific direction." In terms of line segments and points, there are lots of types of projections. The projection of a point on a line and the projection of a line segment connecting two points on a line are the two different types. The point or line in this instance may or may not be a child of the parent line.
Calculating the length of the original line segment as projected on the new line is identical to projecting a line segment connecting two points on a line.

Note: To find the answer to this type of question we need to identify the type or pattern of a question like what are we given like coordinates, length, angle, median or perpendicular given as these types has a bit different way to solve this type of questions.