Express the vector ` vec a=5 hat i-2 hat j+5 hat k` as the sum of two vectors such that one is parallel to the vector ` vec b=3 hat i+ hat k` and other is perpendicular to ` vec bdot`

Express the vector vec a=5hat i-2hat j+5hat k as the sum of two vectors such that one is parallel to the vector vec b=3hat i+hat k and other is perpendicular to vec b .

Express the vector vec(a) = 5 hat (i) - 2 hat (j) + 5 hat (k) as sum of two vectors such that one is parallel to the vector vec(b) = 3 hat(i) + hat (k) and the other is perpendicular to vec(b)

Express the vector vec(a)=(6hat(i)-3hat(j)-6hat(k)) as sum of two vectors such that one is parallel to the vector vec(B)=(hat(i)+hat(j)+hat(k)) and the other is perpendicular to vec(b) .

Resolve the vector vec(b) = hat(i) + hat(j) + hat(k) into vectors parallel and perpendicular to the vector vec(a) = hat(i) + hat(j) .

Find lambda if the vectors vec a=hat i-lambda hat j+3 hat k and vec b=4 hat i-5 hat j+2 hat k are perpendicular to each other.

Prove that the vectors vec a= hat i+ 2 hat j +3 hat k and vec b=2 hat i- hat j are perpendicular.

If vec a=hat i+hat j,vec b=hat j+hat k and vec c=hat k+hat i where unit vectors parallel to vec a+vec b-2vec cdots

If vec a = hat i + hat j, vec b = hat i + hat k, vec c = hat k + hat i, a unit vector parallel to vec a + vec b + vec c

Prove that the vectors vec a = 3 hat i + hat j +3 hat k and vec b = hat i - hat k are perpendicular.