st","extracted_subject":"MATH","extracted_chapter":"COORDINATE GEOMETRY OF THREE DIMENSIONS","extracted_topic":"LINE","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_1924.png?top_left_x=532&top_left_y=777&width=532&height=257&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e71425d76b7ab31e8e1","slug":"the-projection-of-the-line-segment-joining-the-poi-2","content":"The projection of the line segment joining the points (–1, 0, 3) and (2, 5, 1) on the line whose D.R's are 6, 2, 3 is –","options":[{"_id":"68df996f8c3e555ae9e0b62c","text":"\$\\frac{10}{7}\$","sequence":0,"isCorrect":false},{"_id":"68df996f8c3e555ae9e0b62d","text":"\$\\frac{22}{7}\$","sequence":1,"isCorrect":true},{"_id":"68df996f8c3e555ae9e0b62e","text":"\$\\frac{18}{7}\$","sequence":2,"isCorrect":false},{"_id":"68df996f8c3e555ae9e0b62f","text":"None of these","sequence":3,"isCorrect":false}],"correct_answer":"$$\\frac{22}{7}$","explanation":"D.C's of the line are \$\\frac{6}{7},\\frac{2}{7},\\frac{3}{7}\$\n\n\\\\ Projection is (x₂ – x₁) l + (y₂ – y₁) m + (z₂ – z₁)n\n\n= (2 + 1) \$\\frac{6}{7}\$ + (5 – 0) \$\\frac{2}{7}\$ + (1 – 3) \$\\frac{3}{7}\$\n\n= \$\\frac{18}{7} + \\frac{10}{7} - \\frac{6}{7}\$ = \$\\frac{22}{7}\$","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:37.873Z","__v":0,"vector_store_id":"813dadac-1e44-4960-98fc-e76880974016","updated_at":"2024-08-30T21:49:37.873Z","isStarred":false},"params":{"questionSlug":"the-projection-of-the-line-segment-joining-the-poi-2"}}]}]]

Question: The projection of the line segment joining the points (–1, 0, 3) and (2, 5, 1) on the line whose D.R...

Solution