Question

Let's examine the following vectors: ūj = (6,8), ū2 = (5,6) ū = (4, 2, 4) ñ 1 = (7, 3, 1, 3) ja W2 = (7,5, 1, 10). 1. Define vector norms, i.e. lengths. 2. Specify a vector of length 1 and which is parallel to the vector v 3. Find a vector that is perpendicular to the vector Új

Answer 1

The solution is given below

. Define vector nom If I ER is a vector, then Norm of vector i is defined as the length or magnitude of vector and can be calculated by the formal Il Joll = √v, ? + V2 ² + ... +Vn2 Vector Norm is denoted by 11 vll

of length 1 and which is parallel Specify a vector to vector u 7=(4,2,4) vector v let ū be vector of length a which is parallel to Then ū= K (",2,4)= K7 0 We know magnitude of u in 1 - ② Now, we find magnitude of I using equation (1) 1 ūll - J (4K)*+ 2x) +(K) 2 - VICK² +4 K² +16 K² ✓ 36 K2 = 6k ③ Now, comparing 2 and ③ weget 1=6K a k=1 ū = 1 14,2,4) i ū is vector parallel to I of magnitude 1

Find a vector a that is perpendicular to vector u = 16,8) If a vector J is perpendicular to vector then their dot product is o i je u. T o let us take ♡ = (a, b) Then u, V = 0 (6,8). (a, b) =0 - 6a+ 8b=0 - Now this equation has infinite solution take a=1 So we Then G 6 + 8 b=0 86= -6 be – 6 – – 3 3. is a vector perpendicular v = (1, 3) to vector I