The position vectors of the vertices A, B, C of a tetrahedron ABCD are \(\hat{i} + \hat{j} + \hat{k}\), \(\hat{i}\) and \(3\hat{i}\) respectively and the altitude from the vertex D to the opposite face ABC meets the face at E. If the volume of the tetrahedron is \(\dfrac{2\sqrt{2}}{3}\), then the length of DE is:
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Equation of the tangent from the point (3,−1) to the ellipse 2x2 + 9y2 = 3 is
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If , then the values of A1, A2, A3, A4 are
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If S and S' are foci of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, B is the end of the minor axis and B…
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$\lim_{x\to3} \dfrac{\sqrt{3x}-3}{\sqrt{2x-4}-\sqrt{2}}$ is equal to
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The $sin^2 x tanx + cos^2 x cot x-sin2x=1+tanx+cotx $, $x \in (0 , \pi)$, then x
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\(\vec{a}\) and \(\vec{b}\) are non-zero non-collinear vectors such that \(|\vec{a}| = 2\), \(\vec{a}\cdot \vec{b} = 1\…
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Let U and V be two events of a sample space S and P(A) denote the probability of an event A. Which of the following sta…
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If a man purchases a raffle ticket, he can win a first prize of Rs.5,000 or a second prize of Rs.2,000 with probabiliti…
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Let S be the set $\{a\in Z^+:a\leq100\}$.If the equation
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