2 22 marks State whether each statement is true or false Pro

2. (22 marks) State whether each statement is true or false. Provide a brief justification for your answer.

Solution

h) Two non parallel planes with normal vectors u and v intersect in a line parallel to u×v because u×v gives a vector perpedicular to u and v hence u×v is parallel to the point of intersection of plane.

i) No the point should be distinct as well as they should not be collinear only than unique plane is specified.

j) No its not a sphere because x^2+y^2+z^2 = r^2

k) Yes the distance between line x=1and y=1is 2^(1/2). Because we will get a right triangle with perpendicular as 1 and base as 1 hence hypotenous will be 2^(1/2)