00:01
Hello students welcome.
00:02
We have a question here.
00:03
In the first part of the question here, we have to determine whether the statement is true and false.
00:09
Our statement is for any vector, any vector, and v.
00:22
In v3, we need to check this statement as true or not.
00:29
U plus v, absolute value of u plus v is equal to u.
00:35
Plus absolute failure of v.
00:38
So we have to answer whether the statement is true or not.
00:43
So here into the solution of this question, we will take vector u is equal to i minus j vector and next is vector v which is minus i plus j.
01:06
So therefore u plus v is equal to 0 because i will cancel out with i and j will cancel out with j.
01:17
So now absolute value of u plus v is equal to absolute value of 0 that will be equal to 0.
01:31
And now we will, oh sorry, we will calculate value for u.
01:36
This will be equal to square root 1 square plus minus 1 square and the value will be square root of 2.
01:50
Similarly, vector v absolute value will be equal to minus 1 square plus 1 square.
02:00
This is equal to square root of 2.
02:04
So therefore, vector u plus vector v.
02:13
Will be equal to square root of 2 plus square root of 2.
02:18
That will be 2 square root of 2...