The value of \(\hat i\).(\(\hat j\)×\(\hat k\))+\(\hat j\).(\(\hat i\times\hat k\))+\(\hat k\).(\(\hat i\times \hat j\)) is
\(\hat i\).(\(\hat j\)×\(\hat k\))+\(\hat j\).(\(\hat i\)×\(\hat k\))+\(\hat k\).(\(\hat i\)×\(\hat j\))
=\(\hat i.\hat i\).i^+\(\hat j.(-\hat j)\)+\(\hat k.\hat k\)
=1-\(\hat j.\hat j\)+1
=1-1+1
=1
The correct answer is C.
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 |