Question

If the coordinates of $A$ and $B$ be $\left(1,2,3\right)$ and $\left(7,8,7\right)$, then the projections of the line segment $AB$ on the co-ordinate axis are

• A. $6,6,4$
• B. $4,6,4$
• C. $3,3,2$
• D. $2,3,2$

Answer 1

The correct option is A

$6,6,4$

Explanation for the correct option.

Given that, the coordinates of A and B be $\left(1,2,3\right)$ and $\left(7,8,7\right)$,

Let, $\left(x_1,y_1,z_1\right)=\left(1,2,3\right)\mathrm{and}\left(x_2,y_2,z_2\right)=\left(7,8,7\right)$ then, the direction cosine of the line are:

$x_2-x_1=6,y_2-y_1=6,z_2-z_1=4$

And the direction cosines of $x,y,z$ axes are:

$\left(1,0,0\right),\left(0,1,0\right),\left(0,0,1\right)$

Therefore the projection on the coordinate axis gives points, $6,6,4$.

Hence, option A is correct.