st","extracted_subject":"MATH","extracted_chapter":"DETERMINANTS AND MATRICES","extracted_topic":"EXPANSION OF DETERMINANTS, SOLUTION OF EQUATION","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_2164.png?top_left_x=532&top_left_y=391&width=532&height=356&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e74425d76b7ab320b8d","slug":"if-p-q-r-0-a-b-c-then-the-value-of-the-determinant","content":"If p + q + r = 0 = a + b + c, Then the value of the determinant \\(\\left| \\begin{matrix}\npa & qb & rc \\\\\nqc & ra & pb \\\\\nrb & pc & qa\n\\end{matrix} \\right|\\) is","options":[{"_id":"68a3a5b87f15af4716bd294d","text":"0","sequence":0,"isCorrect":true},{"_id":"68a3a5b87f15af4716bd294e","text":"pa + qb + rc","sequence":1,"isCorrect":false},{"_id":"68a3a5b87f15af4716bd294f","text":"1","sequence":2,"isCorrect":false},{"_id":"68a3a5b87f15af4716bd2950","text":"None of these","sequence":3,"isCorrect":false}],"correct_answer":"0","explanation":"∆ = pqr(a³ + b³ + c³) – abc (p³ + q³ + r³) p + q + r = a + b + c = 0 ⇒ p³ + q³ + r³ = 3pqr, a³ + b³ + c³ = 3abc\n\n∆ = 3pqr abc – 3abc pqr = 0","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:40.083Z","__v":0,"vector_store_id":"90db7086-8b67-424e-9fb0-0ac8be94e4f0","updated_at":"2024-08-30T21:49:40.083Z","isStarred":false},"params":{"questionSlug":"if-p-q-r-0-a-b-c-then-the-value-of-the-determinant"}}]}]]

Question: If p + q + r = 0 = a + b + c, Then the value of the determinant \(\left| \begin{matrix} pa & qb & rc...

Solution