Question

Show that the vectors A = 2i + 5j – 3k and B = 4i + 10 j – 6 k are parallel.

Answer 1

Explanation:

2/4=5/10=-3/-6

1/2=1/2=1/3

A vector is ai+bj+ck and B vector is xi+yj+zk , and if they are parallel , a/x=b/y=c/z and if they are perpendicular , ax+by+cz=0

Answer 2

Answer:

It's simple I'll just explain how it's done them you can try it yourself.

first see both vectors you can notice that vector B is nothing but addition of A and some vector P=

2i+5j-3k

that is it's simply Vector A plus vector A

since we are adding vector A to itself that means the direction is not changed .

therefore this new vector P=A+A makes similar angles with each axis x,y,z as A

since P=B

therefore they make an angle of zero degrees with each other.

hence they are parallel.

hope it helped.