3D Vectors, Check my answers please?

Question

Check my answers please:

a = 4i + 3j
b = 2i - j
c = 2i + j + 3 k
d = 2i - 2j + k

Questions & Answers:

(a) 2a + 5b = 18i + j
(b) a.b = 5
(c) a x b = -10 k

Answer 1

(a) correct
(b) correct
(c) correct

Answer 2

All planes of the form 2x - y + 3z = d are going to be parallel. you are able to think of of the d as a parameter which shifts the plane lower back and forth alongside that ordinary vector, giving planes which bypass the commencing place at diverse distances. useful values of d will bypass the commencing place on one edge, detrimental values will supply planes that bypass on the different edge. d provides the minimum distance in case you normalize the equation, writing it interior the form ax + by using + cz = d the place (a, b, c) is a unit vector. to try this, divide the two sides by using the magnitude of (2, -a million, 3). So the plane 2x -y + 3z = a million passes the commencing place at a distance of a million/|(2, -a million, 3)|

Answer 3

all Three are correct

Answer 4

All the three are correct
but please tell me that why you have mentioned c and d vectors