alleryStart learning →The direction ratios of the line joining the points $(1,2,3)$ and $(4,5,6)$ are:
- $4, 5, 6$
- $3, 3, 3$
- $1, 2, 3$
- $5, 7, 9$
Show answer and solution
Correct answer: B. $3, 3, 3$
Direction ratios = differences of coordinates: (4−1, 5−2, 6−3) = (3,3,3).
Indian Navy INET Three Dimensional Geometry — practice questions
Explore 27 free Three Dimensional Geometry questions in Indian Navy INET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
Practise Three Dimensional Geometry with Quill →Three Dimensional Geometry questions and exercises with answers
Showing questions 1–27 of 27.
The direction ratios of the line joining the points $(1,2,3)$ and $(4,5,6)$ are:Read the answer and worked solution →The cosine of the angle between two lines with direction ratios $(1,2,2)$ and $(2,2,1)$ is:Read the answer and worked solution →Match each term to its definitionRead the answer and worked solution →True or false: direction cosinesRead the answer and worked solution →Direction cosines or direction ratios?Read the answer and worked solution →Order the steps: direction ratios to direction cosinesRead the answer and worked solution →Skew linesRead the answer and worked solution →Tap every pair of lines that could be skewRead the answer and worked solution →Match each equation to what it describesRead the answer and worked solution →Complete the definition of direction cosinesRead the answer and worked solution →Complete the definition of skew linesRead the answer and worked solution →True or false: angles between linesRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Reading the equationsRead the answer and worked solution →Flip and pair: symbol with meaningRead the answer and worked solution →Same plane or different planes?Read the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Order the steps: angle between two lines from direction ratiosRead the answer and worked solution →Tap each statement that is true of a line's equationRead the answer and worked solution →True or false: reading the chapter's scopeRead the answer and worked solution →Match each condition to what it meansRead the answer and worked solution →The normalising relationRead the answer and worked solution →Spot the odd one outRead the answer and worked solution →Assertion and reason: equations of a lineRead the answer and worked solution →Which quantity is which?Read the answer and worked solution →
Worked practice questions
The cosine of the angle between two lines with direction ratios $(1,2,2)$ and $(2,2,1)$ is:
- $\tfrac{4}{9}$
- $\tfrac{2}{3}$
- $\tfrac{1}{9}$
- $\tfrac{8}{9}$
Show answer and solution
Correct answer: D. $\tfrac{8}{9}$
We have cosθ = (1·2+2·2+2·1)/(√9·√9).
So cosθ = 8/9.
Match each term to its definition
Read exercise and reference answers
- Matching pairs
- Left
- Direction cosines
- Right
- cosines of the angles a line makes with the axes
- Left
- Direction ratios
- Right
- numbers proportional to the direction cosines
- Left
- Skew lines
- Right
- lines that neither meet nor run parallel
- Left
- l² + m² + n²
- Right
- always equals 1
The chapter's four core definitions, taken straight from the summary. Source: syllabus Maths Part II, Ch 11 Three Dimensional Geometry.
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