The line l₁ has equation r = i+3j-k+λ(i−j−4k). The plane Π contains l₁ and is parallel to the vector 2i+5j-4k. The line l₂ is parallel to the vector 5i – 5j – 2k.

The line \( l_1 \) passes through the point with position vector \( 8\mathbf{i} + 8\mathbf{j} - 7\mathbf{k} \) and is…

Answer only one of the following two alternatives. EITHER Show that ∫ (from 0 to π) eˣ sin x dx = (1 + e^π) / 2. Giv…

Answer only one of the following two alternatives. OR The position vectors of the points A, B, C, D are 2i + 4j – 3k…

Use de Moivre's theorem to show that cos 4θ = 8 cos⁴ θ – 8 cos² θ + 1.

The curve C has parametric equations x = ⅓t³ – ln t, y = ⅔t³, for 1 ≤ t ≤ 3.

Write down the eigenvalues of the matrix A, where A = [[1, 4, -16], [0, 2, 3], [0, 0, 3]]