Find the scalar components and magnitude of the vector joining the points\( P(x_{1},y_{1},z_{1})and Q(x_{2},y_{2},z_{2}).\)
The vector joining the points P(x1,y1,z1)and Q(x2,y2,z2)can be obtained by,
\(\overrightarrow{PQ}=\)position vector of \(Q-\)Position vector of \(P\)
\(=(x_{2}-x_{1})\hat{i}+(y_{2}-y_{1})\hat{j}+(z_{2}-z_{1})\hat{k}\)
|\(\overrightarrow{PQ}\)|\(=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}+(z_{2}-z_{1})^{2}}\)
Hence,the scalar components and the magnitude of the vector joining the given points are respectively{\((x_{2}-x_{1}),(y_{2}-y_{1}),(z_{2}-z_{1})\)}and \(\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}+(z_{2}-z_{1})^{2}}.\)
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 |