Classify the following measures as scalars and vectors.
(i)10kg
(ii)2metres north-west
(iii)40°
(iv)40watt
(v)10-19coulomb
(vi)20m/s2
(i)10kg is a scalar quantity because it involves only magnitude.
(ii) 2 meters north-west is a vector quantity as it involves both magnitude and direction.
(iii)40°is a scalar quantity as it involves only magnitude.
(iv)40 watts is a scalar quantity as it involves only magnitude.
(v)10-19 coulomb is a scalar quantity as it involves only magnitude.
(vi)20m/s2 is a vector quantity as it involves magnitude as well as direction.
If \( X \) is a random variable such that \( P(X = -2) = P(X = -1) = P(X = 2) = P(X = 1) = \frac{1}{6} \), and \( P(X = 0) = \frac{1}{3} \), then the mean of \( X \) is
List-I | List-II |
---|---|
(A) 4î − 2ĵ − 4k̂ | (I) A vector perpendicular to both î + 2ĵ + k̂ and 2î + 2ĵ + 3k̂ |
(B) 4î − 4ĵ + 2k̂ | (II) Direction ratios are −2, 1, 2 |
(C) 2î − 4ĵ + 4k̂ | (III) Angle with the vector î − 2ĵ − k̂ is cos⁻¹(1/√6) |
(D) 4î − ĵ − 2k̂ | (IV) Dot product with −2î + ĵ + 3k̂ is 10 |
In general, vectors are used in Maths and Science and are categorized into 10 different types of vectors such as:-