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Find the equation of the line that passes through A and B

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Reference no: EM132344765

Calculus and Matrix Algebra Assignment -

Show all working and give answers exactly where possible.

Q1. If a = (3, 1, 3) and b = (4, -1, 8), find |a|, |b|, 3a - b, a · b, a x b and b x a. What is the angle between a and b?

Q2. For the triangle ABC, with vertices A = (2, -2, 3), B = (5, 1, 6) and C = (8, v, 3), find

(a) the length of side AB,

(b) the equation of the line that passes through A and B,

(c) the value of v so that the angle at point B is π/3.

Q3. Solve the following system of equations using row reductions (Show all working).

2x + 4y + z = 29, x + y + 2z = 7, x + y + 3z = 6.

Q4. Use row operations (show all working) to compute the inverse of the matrix A. Show that it is correct (to get full marks you must do this).

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Q5. Find the equation of the plane containing the vectors a = (1, 2, 4) and b = (6, 1, 4) and the point A(6, 7, -3).

Q6. Find the equation of the line from A(1, 7, -6) to B(-1, 2, -1) in parametric form.

Q7. Suppose a jump-jet takes off perpendicular to the deck of an air-craft carrier whose surface is described by 2x - 5y + 6z = 14. In what direction will it launch? If it takes off vertically (in the direction of k), what is the angle between this direction and the normal to the deck?

Reference no: EM132344765

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