Vectors a = (3, 4) and b = (m, 2) are given. For which value of m they are perpendicular?

The value of m is .

Step-by-step explanation:

If two vectors and are perpendicular to each other then their dot product will be zero i.e

If two vectors and are parallel to each other then their cross product will be zero i.e

Given vectors are a= (3,4) and b=(m,2)

The position vector of  is =

The position vector of  is =

Since and are perpendicular.

Then,

⇒3.m +4.2=0

⇒3m+8=0

⇒3m= -8

The value of m is .

(-1,-0.5)

step-by-step explanation:

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.