Three Dimensional Geometry - Online Test

Answer : Option A
Explaination / Solution:

Equation of a line through a point (x1, y1, z1) and having direction cosines l, m, n is given by : x−x1l=y−y1m=z−z1n

Answer : Option D
Explaination / Solution:

Vector equation of a line that passes through two points whose position vectors are  is given by:  

Answer : Option C
Explaination / Solution:

Cartesian equation of a line that passes through two points (x1, y1, z1) and (x2, y2, z2)is given by :x−x1x2−x1=y−y1y2−y1=z−z1z2−z1 .

Answer : Option C
Explaination / Solution:

Answer : Option B
Explaination / Solution:

Shortest distance between two skew lines is The line segment perpendicular to both the lines .

Answer : Option A
Explaination / Solution:

Shortest distance between r⃗ =a1→+λb2→andr⃗ =a1→+μb2→
is given by :

Answer : Option B
Explaination / Solution:

Shortest distance between the lines x−x1a1=y−y1b1=z−z1c1and x−x1a2=y−y1b2=z−z1c2is given by: 

Answer : Option D
Explaination / Solution:

If a line makes angles 90∘, 135∘, 45∘ with the x, y and z – axes respectively, then the direction cosines of this line is given by :

Answer : Option A
Explaination / Solution:

If a line has the direction ratios – 18, 12, – 4, then its direction cosines are given by:

Answer : Option D
Explaination / Solution:

The equation of the line which passes through the point (1, 2, 3) and is parallel to the vector
3i^+2j^−2k^ , let vector a→=iˆ+jˆ+kˆ and vector b→=3i^+2j^−2k^, 
the equation of line is :
a→+λb→=(iˆ+jˆ+kˆ)+λ(3i^+2j^−2k^).