If a,b,c are there mutually perpendicular vectors, then a+b+c is equal to

Answer 1

Since a, b, and c are mutually perpendicular vectors, their dot products with each other would be zero.

Therefore, (a+b+c) • (a+b+c) = a • a + a • b + a • c + b • a + b • b + b • c + c • a + c • b + c • c

= ||a||^2 + ||b||^2 + ||c||^2

Since a, b, and c are mutually perpendicular, their magnitudes are equal. Let this value be k.

Therefore, (a+b+c) • (a+b+c) = k^2 + k^2 + k^2

= 3k^2

Hence, a+b+c = sqrt(3)k