State with reasons, whether the following algebraic operations with scalar and vector physical quantities are meaningful:
(a) adding any two scalars,
(b) adding a scalar to a vector of the same dimensions,
(c) multiplying any vector by any scalar,
(d) multiplying any two scalars,
(e) adding any two vectors,
(f) adding a component of a vector to the same vector
State with reasons, whether the following algebraic operations with scalar and vector physical quantities are meaningful:
(a) adding any two scalars,
(b) adding a scalar to a vector of the same dimensions,
(c) multiplying any vector by any scalar,
(d) multiplying any two scalars,
(e) adding any two vectors,
(f) adding a component of a vector to the same vector
Solution and Explanation
a) adding any two scalars - Meaningful
Explanation: The addition of two scalar quantities is meaningful only if they both represent the same physical quantity.
(b) adding a scalar to a vector of the same dimensions - Not Meaningful
Explanation: The addition of a vector quantity with a scalar quantity is not meaningful.
(c) multiplying any vector by any scalar - Meaningful
Explanation: A scalar, irrespective of the physical quantity it represents, can be multiplied with another scalar having the same or different dimensions.
(d) multiplying any two scalars - Meaningful
Explanation: A scalar, irrespective of the physical quantity it represents, can be multiplied with another scalar having the same or different dimensions.
(e) adding any two vectors - Meaningful
Explanation: The addition of two vector quantities is meaningful only if they both represent the same physical quantity.
(f) adding a component of a vector to the same vector - Meaningful
Explanation: A component of a vector can be added to the same vector as they both have the same dimensions.
Top Questions on Motion in a plane
- The speed \( v \) of a wave on a string depends on the tension \( F \) in the string and the mass per unit length \( m/L \) of the string. If it is known that [F] = [ML][T]–2, the values of the constants \( a \) and \( b \) in the following equation for the speed of a wave on a string are: \[ v = (\text{constant}) F^a \left( \frac{m}{L} \right)^b \]
- OJEE - 2024
- Physics
- Motion in a plane
y = a sin(βx + γt)wherex and t represent displacement and time, respectively. Then, the dimensional formula for β— γis:
- TS EAMCET - 2024
- Physics
- Motion in a plane
- The time period of a simple pendulum on the surface of the earth is \( T \). The time period of the same pendulum at a height of 1280 km from the surface of the earth is
- TS EAMCET - 2024
- Physics
- Motion in a plane
- A body thrown vertically upwards with certain velocity from the ground reaches a maximum height \( H \). The ratio of the times at which the body is at a height of \( \frac{H}{2} \) is:
- TS EAMCET - 2024
- Physics
- Motion in a plane
- The theory currently accepted as proper framework for explaining microscopic phenomena is
- TS EAMCET - 2024
- Physics
- Motion in a plane
Questions Asked in CBSE Class XI exam
- Find \((x + 1)^6 - (x - 1)^6\). Hence or otherwise evaluate \((\sqrt2 + 1)^6 + (\sqrt2 - 1)^6.\)
- CBSE Class XI
- Binomial Theorem for Positive Integral Indices
- If U = {a, b, c, d, e, f, g, h}, find the complements of the following sets:
(i) A = {a, b, c}
(ii) B = {d, e, f, g}
(iii) C = {a, c, e, g}
(iv) D = {f, g, h, a}- CBSE Class XI
- Complement of a Set
- Consider the following species: N3- , O2-, F-, Na+, Mg2+ and Al3+
- What is common in them?
- Arrange them in the order of increasing ionic radii.
- CBSE Class XI
- Modern Periodic Law And The Present Form Of The Periodic Table
- Find and write down structures of 10 interesting small molecular weight biomolecules. Find if there is any industry which manufactures the compounds by isolation. Find out who are the buyers.
- CBSE Class XI
- How To Analyse Chemical Composition?
- How many litres of water will have to be added to 1125 litres of the 45% solution of acid so that the resulting mixture will contain more than 25% but less than 30% acid content?
- CBSE Class XI
- inequalities