Question

A vector A of magnitude 6 and another vector B have a resultant magnitude 12. The vector B:

a. must have a magnitude of at least 6 but no more than 18
b. may have a magnitude of 20
c. cannot have a magnitude greater than 12
d. must be perpendicular to A

the formula for resultant vector is \[R = \sqrt{A^2 + B^2}\]isn't it?

Answer 1

that only works if the triangle of vector A, vector B, & vector R form a Right Triangle

Answer 2

think about using the rules for making triangles to assist you in this problem

Answer 3

don't all vectors form right triangles?

Answer 4

no, i will draw one that doesn't

Answer 5

i guess that's a point...so what's the general idea then?

Answer 6

if the formula you have written words than your answer is d

Answer 7

The sum of two sides of a triangle cannot be less than the remaining side

Answer 8

i meant with vectors

Answer 9

if both vectors are in the same direction then the second could be of magnitude 6
so 6+6=12
if in a perpendicular direction then
\[\sqrt {6^2+x^2}=12\]
or
\[x^2=108\]
\[x=10.39\]
@lgbasallote do you get the idea?

Answer 10

that's the idea there too?

Answer 11

what's that 6 + 6 = 12 for?

Answer 12

if they are in the same direction

Answer 13

you lost me there..i do know that the third side could be 10.38...

Answer 14

anyway...why is B perpendicular to A again @juantweaver ?

Answer 15

@lgbasallote sorry I made a mistake, let me see it again