In figure, identify the following vectors.
(i)Coinitial (ii)Equal (iii)Collinear but not equal
(i)Vectors a→and d→are coinitial because they have the same initial point.
(ii)Vectors b→and d→are equal because they have the same magnitude and direction.
(iii)Vectors a→and c→are collinear but not equal.This is because although they are parallel, their directions are not the same.
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:-