Solve question number 4

Tutorial questions 1). If a = i - 7j + 7k and b = 3i - 2j + 2k. Find a x b and (a x 6) 2). Find A and / if (2i + 6j + 27k) x (i + >j + uk) = 0 3) Given that a = 2i + 4j + Ak and b = i + 2j + 7k, determine > such that a and b are orthogonal. 4) Let (4, 0, 0), (2, 6,0) and (1, 4, 2) be position vectors of points A, B and C respec- tively i) Find the cosine of an angle between BA and BC ii) Find the area of a triangle ABC 5) If a = 5i - j -3k and b = i + 3i - 5k then show that the vectors a + b and a - b are perpendicular. 6) Find the angle between the vectors i - 2j + 3k and 3i - 2j + k 7) Find the dot product of vectors i + 2j - 3/ and 2i - j + k 8) Find the vector joining the points P(2, 3, 0) and Q(-1, -2,4) and also direction cosines of PQ 9) Find the unit vector in a direction of 2 + 3j + k 10) If a = i + 2j and b = 2i + j show that a = b 11) Find the volume of the parallelepiped defined by a = 67+3j -2k,b = -4i+6j+9k and c = 3i + 3j - 11k 12) Find the volume of parallelepiped with adjacent edges v, w and u, 7 = (5, 1, 2), wii = (1,4,3) and u = (2,3, 6) 13) Find area of parallelepiped whose adjacent sides are 2i - 4j + 4k and i - 2j - 3k 14) Find the scalar triple product of vectors i + 2j + 3k, -i - j + k and i + j + k 15) Find the area of triangle ABC whose vertices are A(2, 1, 1), B(3, 2, 1) and C(-2, -4, 1). 16) a = 2i + 6j + 3k and b = i + 2j + 2k find the angle between a and b use cross product @ 2024 DAR ES SALAAM INSTITUTE OF TECHNOLOGY