JEE Exam > JEE Questions > Consider A, B, C and D with position vectors ...
Start Learning for Free
Consider A, B, C and D with position vectors 7î - 4ĵ + 7k̂, î - 6ĵ + 10k̂, -î -3ĵ + 4k̂ and 5î - ĵ + 5k̂ respectively. Then ABCD is a
- a)rhombus
- b)rectangle
- c)square
- d)none of these
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
Consider A, B, C and D with position vectors 7i - 4j + 7k, i - 6j + 10...
Given Information:
- Position vectors of points A, B, C, and D are 7i - 4j + 7k, i - 6j + 10k, -i - 3j + 4k, and 5i - j + 5k respectively.
Explanation:
Calculating Vectors AB, BC, CD, and DA:
- Vector AB = Position vector of B - Position vector of A = (i - 6j + 10k) - (7i - 4j + 7k) = -6i + 2j + 3k
- Vector BC = Position vector of C - Position vector of B = (-i - 3j + 4k) - (i - 6j + 10k) = -2i + 3j - 6k
- Vector CD = Position vector of D - Position vector of C = (5i - j + 5k) - (-i - 3j + 4k) = 6i + 2j + k
- Vector DA = Position vector of A - Position vector of D = (7i - 4j + 7k) - (5i - j + 5k) = 2i - 3j + 2k
Checking for Parallelogram:
- For a parallelogram, opposite sides should be parallel.
- AB is not parallel to CD and BC is not parallel to DA.
- Hence, ABCD is not a parallelogram.
Checking for Rhombus/Rectangle/Square:
- For a rhombus, all sides should have equal length.
- For a rectangle, opposite sides should be equal in length and all angles should be 90 degrees.
- For a square, all sides should have equal length and all angles should be 90 degrees.
- The sides AB, BC, CD, and DA have different lengths and angle conditions are not satisfied.
- Therefore, ABCD is none of these (a rhombus, rectangle, or square).
Therefore, the correct answer is option 'D' - none of these.
- Position vectors of points A, B, C, and D are 7i - 4j + 7k, i - 6j + 10k, -i - 3j + 4k, and 5i - j + 5k respectively.
Explanation:
Calculating Vectors AB, BC, CD, and DA:
- Vector AB = Position vector of B - Position vector of A = (i - 6j + 10k) - (7i - 4j + 7k) = -6i + 2j + 3k
- Vector BC = Position vector of C - Position vector of B = (-i - 3j + 4k) - (i - 6j + 10k) = -2i + 3j - 6k
- Vector CD = Position vector of D - Position vector of C = (5i - j + 5k) - (-i - 3j + 4k) = 6i + 2j + k
- Vector DA = Position vector of A - Position vector of D = (7i - 4j + 7k) - (5i - j + 5k) = 2i - 3j + 2k
Checking for Parallelogram:
- For a parallelogram, opposite sides should be parallel.
- AB is not parallel to CD and BC is not parallel to DA.
- Hence, ABCD is not a parallelogram.
Checking for Rhombus/Rectangle/Square:
- For a rhombus, all sides should have equal length.
- For a rectangle, opposite sides should be equal in length and all angles should be 90 degrees.
- For a square, all sides should have equal length and all angles should be 90 degrees.
- The sides AB, BC, CD, and DA have different lengths and angle conditions are not satisfied.
- Therefore, ABCD is none of these (a rhombus, rectangle, or square).
Therefore, the correct answer is option 'D' - none of these.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
Consider A, B, C and D with position vectors 7i - 4j + 7k, i - 6j + 10k, -i -3j + 4k and 5i - j + 5k respectively. Then ABCD is aa)rhombusb)rectanglec)squared)none of theseCorrect answer is option 'D'. Can you explain this answer?
Question Description
Consider A, B, C and D with position vectors 7i - 4j + 7k, i - 6j + 10k, -i -3j + 4k and 5i - j + 5k respectively. Then ABCD is aa)rhombusb)rectanglec)squared)none of theseCorrect answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Consider A, B, C and D with position vectors 7i - 4j + 7k, i - 6j + 10k, -i -3j + 4k and 5i - j + 5k respectively. Then ABCD is aa)rhombusb)rectanglec)squared)none of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider A, B, C and D with position vectors 7i - 4j + 7k, i - 6j + 10k, -i -3j + 4k and 5i - j + 5k respectively. Then ABCD is aa)rhombusb)rectanglec)squared)none of theseCorrect answer is option 'D'. Can you explain this answer?.
Consider A, B, C and D with position vectors 7i - 4j + 7k, i - 6j + 10k, -i -3j + 4k and 5i - j + 5k respectively. Then ABCD is aa)rhombusb)rectanglec)squared)none of theseCorrect answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Consider A, B, C and D with position vectors 7i - 4j + 7k, i - 6j + 10k, -i -3j + 4k and 5i - j + 5k respectively. Then ABCD is aa)rhombusb)rectanglec)squared)none of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider A, B, C and D with position vectors 7i - 4j + 7k, i - 6j + 10k, -i -3j + 4k and 5i - j + 5k respectively. Then ABCD is aa)rhombusb)rectanglec)squared)none of theseCorrect answer is option 'D'. Can you explain this answer?.
Solutions for Consider A, B, C and D with position vectors 7i - 4j + 7k, i - 6j + 10k, -i -3j + 4k and 5i - j + 5k respectively. Then ABCD is aa)rhombusb)rectanglec)squared)none of theseCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of Consider A, B, C and D with position vectors 7i - 4j + 7k, i - 6j + 10k, -i -3j + 4k and 5i - j + 5k respectively. Then ABCD is aa)rhombusb)rectanglec)squared)none of theseCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Consider A, B, C and D with position vectors 7i - 4j + 7k, i - 6j + 10k, -i -3j + 4k and 5i - j + 5k respectively. Then ABCD is aa)rhombusb)rectanglec)squared)none of theseCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for Consider A, B, C and D with position vectors 7i - 4j + 7k, i - 6j + 10k, -i -3j + 4k and 5i - j + 5k respectively. Then ABCD is aa)rhombusb)rectanglec)squared)none of theseCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of Consider A, B, C and D with position vectors 7i - 4j + 7k, i - 6j + 10k, -i -3j + 4k and 5i - j + 5k respectively. Then ABCD is aa)rhombusb)rectanglec)squared)none of theseCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Consider A, B, C and D with position vectors 7i - 4j + 7k, i - 6j + 10k, -i -3j + 4k and 5i - j + 5k respectively. Then ABCD is aa)rhombusb)rectanglec)squared)none of theseCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup