1. For two vectors to be equal they should have the _________. (a) same magnitude (b) same direction (c) same magnitude and direction (d) same magnitude but opposite direction 2. A... 1. For two vectors to be equal they should have the _________. (a) same magnitude (b) same direction (c) same magnitude and direction (d) same magnitude but opposite direction 2. A unit vector in the direction of the negative of the vector -i + j + k is _________. (a) 1/√3 (i + j - k) (b) i + j - k (c) √3/3 (i + j - k) (d) -1/√3 (i + j - k) 3. If a = 2i + j + k, b = -i + j + k, then a . b = _________. (a) 7 (b) -7 (c) 4 (d) -4 4. Masses of three pieces of wires made of the same metal are in the ratio 1:3:5 and their lengths are in (a) 1:3:5 (b) 5:3:1 (c) 1:15:125 (d) 125:15:1 5. Out of the following ________ is an ohmic conductor. (a) transistor (b) vacuum tube (c) electrolyte (d) nichrome wire 6. In parallel combination of resistances, the equivalent resistance is _________. (a) larger than the largest of individual resistance (b) smaller than the smallest of the individual resistance (c) has median value (d) value is decided by the applied emf.
Understand the Problem
The question is asking for the correct answers to a series of multiple-choice physics questions focused on vectors, resistances, and properties of conductors.
Answer
1: Same magnitude and direction. 2: -1/√3 (i+j-k). 3: 4. 4: 5:3:1. 5: Nichrome wire. 6: Smaller than smallest.
["(1) For two vectors to be equal, they should have the: same magnitude and direction.","(2) A unit vector in the direction of the negative of the vector -i + j + k is: -1/\u221a3 (i + j - k).","(3) If a = 2i + j + k, b = -i + j + k, then a . b = 4.","(4) Masses of pieces of wire in ratio 1:3:5, resistances are in ratio: 5:3:1.","(5) Out of the following, nichrome wire is an ohmic conductor.","(6) In parallel combination of resistances, the equivalent resistance is: smaller than the smallest of the individual resistance."]
Answer for screen readers
["(1) For two vectors to be equal, they should have the: same magnitude and direction.","(2) A unit vector in the direction of the negative of the vector -i + j + k is: -1/\u221a3 (i + j - k).","(3) If a = 2i + j + k, b = -i + j + k, then a . b = 4.","(4) Masses of pieces of wire in ratio 1:3:5, resistances are in ratio: 5:3:1.","(5) Out of the following, nichrome wire is an ohmic conductor.","(6) In parallel combination of resistances, the equivalent resistance is: smaller than the smallest of the individual resistance."]
More Information
To solve for the unit vector, you must reverse the given vector and normalize it by its magnitude. The dot product checks orthogonality or other properties of vectors. Ohmic conductors obey Ohm’s Law with a constant resistance.
Tips
In vector problems, ensure to correctly calculate dot products and unit vectors by following the steps methodically.
Sources
- For two vectors to be equal, they should - shaalaa.com
- Any two vectors that have the same direction and magnitude - quora.com
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