1 thought on “Ex L Find a vector in the direction of a = i – j that has magnitude 7 units.”
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:
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−−−−−−−−√