Question

Consider the following statements:

1. A-line in space can have infinitely many direction ratios.

2. It is possible for certain lines that the sum of the squares of direction cosines can be equal to some of its direction cosines.

Which of the above statements is/are correct?

1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2

Answer 1

Correct Answer - Option 1 : 1 only

Concept:

Direction cosine:

Direction cosines are the cosines of the angles made by a directed line segment with the coordinate axes. 

The sum of the square of direction cosine always 1.

Direction Ratio:

• If a, b, c are three numbers proportional to the direction cosine l, m, n of a straight line, then a, b, c are called its direction ratios.
• They are also called direction numbers or direction components.
• Direction cosines of a line are unique but direction ratios of a line in no way unique but can be infinite.

 

Explanation:

Statement: 1

The direction cosines for any line must be unique. However, there are infinitely many sets of direction ratios since direction ratios are just a set of any three numbers proportional to the direction cosines.

Statement: 2

We know that, the sum of the squares of the direction cosines is equal to one.

∴ Only statement 1 is correct.