Questions and Answers
The vector joining the points A (1, 1, –1) and B (2, –3, 4) & pointing from A to B is -
If the directions of vectors a and b are interchanged, then the resultant will have the same:
The vector sum of the forces of 10 N and 6 N can be:
Given: C = A + B. The angle between A and B is:
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The sum and difference of two perpendicular vectors of equal lengths are:
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Three non-zero vectors A, B, and C satisfy the relation A.B = 0 & A.C = 0. Then A can be parallel to:
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The angle between two vectors with a scalar product of 8 and a vector product of 8√3 is:
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Which of the following sets of displacements might be capable of bringing a car to its returning point?
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If vector A points vertically downward & vector B points towards east, then the vector product A x B is:
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Given: a + b + c = 0. If two of the vectors are equal in magnitude, the angles between the vectors are:
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A fly starting at one corner of a hall measuring 10 m × 12 m × 14 m ends up at a diametrically opposite corner. The magnitude of its displacement is nearly:
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In Figure, E + D - C equals...
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Study Notes
Vector Operations and Properties
- The vector from point A (1, 1, -1) to point B (2, -3, 4) is calculated by subtracting the coordinates, resulting in: î + 4ĵ + 5k̂.
- The resultant vector of two vectors a and b, inclined at an angle θ, changes when their directions are interchanged; however, the magnitude remains the same.
Resultant Forces and Magnitudes
- Vector sum of forces can vary based on direction:
- Example: Forces of 10 N and 6 N can yield resultant values of 2 N, 8 N, 18 N, or 20 N depending on the angle between them.
- Given magnitudes A (12), B (5), and C (13), the angle between A and B can be derived from the law of cosines.
Vector Relations and Properties
- The sum and difference of two perpendicular vectors of equal lengths yields resultant vectors that are also perpendicular and of equal length.
- For three non-zero vectors A, B, and C, if A is perpendicular to both B and C (A·B = 0 and A·C = 0), A may be parallel to the cross product of B and C.
Scalar and Vector Product
- The magnitude of the scalar product of two vectors being 8 and the vector product being (8\sqrt{3}) leads to the calculation of the angle between them—possible angles include 30º, 60º, 120º, or 150º.
Displacement and Return Points
- A set of displacements that returns the car to its starting point must satisfy the triangle inequality.
- Example displacements to check include various combinations varying from 5 km to 200 km.
Vector Direction and Cross Product
- A vector A pointing downward and vector B pointing east results in a vector product A × B that is directed west.
Equality of Vectors
- In a closed triangle formation (a + b + c = 0), when two vectors are of equal magnitude and the third vector's magnitude is double, the angles between them can vary; possible configurations include angles of 90º, 135º, and 60º.
Displacement in Three-Dimensional Space
- The displacement magnitude from one corner of a hall with dimensions 10 m × 12 m × 14 m to the opposite corner can be calculated using the Pythagorean theorem, resulting in a magnitude close to 17 m.
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Description
Enhance your IIT-JEE preparation with these daily practice problems in physics. Designed by top educators, this quiz covers critical concepts and problem-solving strategies crucial for success in the exam. Test your knowledge and improve your skills with challenging questions that reflect the IIT-JEE syllabus.
