If the projections of a line segment on the x, y and z axes in 3-dimensional space are 2, 3 and 6 respectively, then the length of line segment is

Question

If the projections of a line segment on the x, y and z axes in 3-dimensional space are 2, 3 and 6 respectively, then the length of line segment is (A) 6 (B) 7 (C) 9 (D) 12

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/a456101594ab6983b0c50791716255a3-.png" /> ∴ AB =√( x 1- x 2)2+( y 1- y 2)2+( z 1- z 2)2=√4+9+36=√49=7

Q. If the projections of a line segment on the x, y and z axes in 3-dimensional space are 2, 3 and 6 respectively, then the length of line segment is

6

7

9

12

$∴ A B = (x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2} + (z_{1} - z_{2})^{2} = 4 + 9 + 36 = 49 = 7$

Q. If the projections of a line segment on the x, y and z axes in 3-dimensional space are 2, 3 and 6 respectively, then the length of line segment is

6

7

9

12

∴AB=(x1​−x2​)2+(y1​−y2​)2+(z1​−z2​)2​=4+9+36​=49​=7

$∴ A B = (x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2} + (z_{1} - z_{2})^{2} = 4 + 9 + 36 = 49 = 7$