Question

Ex L Find a vector in the direction of a = i - j that has magnitude 7 units.​

Answer 1

Answer:

What you need is a vector (say  x⃗ )  whose magnitude is 7 and direction is in the direction of  a⃗   ,where you have  a⃗ =i^−2j^  

A unit vector in the direction of  a⃗   is  a^ . It has magnitude 1, and direction of  a⃗  . Put seven of these together, and you get the answer. Putting seven vectors in a line means vectorially adding them seven times, i.e., multiply by 7! Your answer is

x⃗ =7a^  

Now, how to find  a^ ?

Just like multiplying with 7 increases the magnitude to 7 times, diving a vector by it’s magnitude will bring the vector’s magnitude to 1. So, we get:

a^=1|a⃗ |a⃗ .  

|a⃗ |=ax2+ay2−−−−−−−−√