Maths Task

P3 Let a, b, c, and d be vectors in R and let λ be a scalar. For each of the following expressions determine whether the result makes sense, and if so, whether it is a scalar or a vector. Explain briefly your answers.

 

(a) d x (č (a x b));

 

(b) (č x (a x b)) d;

 

(c) (1+ă.bč;

 

(d) cx (projåb + 1);

 

(e) (ã – b + ||č|| ) a – (b x d).

 

 

P5 Given the following lines in R’,

 

li: ={ х 2 + 3t 5 + 2t 1

 

4 – 4s y = 5 + 4s 2 = -2 + s.

 

(a) calculate the distance between two lines li and la;

 

(b) write down the normal equation of the plane passing through the point (2, 5, 1) of l1

 

and perpendicular to l1;

 

(c) find the distance from (1,1,1) to the plane from (b) above.

 

Remark. In (a) and (c) give the exact answers in radicals (i.e., using square roots);