VECTOR Question help please! (VERY BASIC) :]

A vector = 0.4i + 0.8j + ck is a unit vector then value of c is:

a) √0.2
b) √0.8

Please help me! Exams approaching.. It'll be really appreciated and awarded with 10 pts. in return

Thank you in advance~~ (:

The definition of a unit vector is that it has a magnitude equal to 1. We find the magnitude of a vector v = ai + bj + ck using the distance formula,

||v|| = sqrt(a^2 + b^2 + c^2)

So, if v is a unit vector, ||v|| = 1,

1 = sqrt(a^2 + b^2 + c^2)

For your vector, you have a = 0.4 and b = 0.8. Let's plug those in to find the value of c.

1 = sqrt(0.4^2 + 0.8^2 + c^2)
1^2 = 0.4^2 + 0.8^2 + c^2
1 - 0.4^2 - 0.8^2 = c^2
c = ±sqrt(1 - 0.4^2 - 0.8^2)
c = ±sqrt(1 - 0.16 - 0.64)
c = ±sqrt(0.2)

There's your answer. Note that either a positive or negative square root is acceptable (in other words, the vector could point in either direction). I hope that helps!

Thanks!

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It's length must be 1 as it is a unit vector. It's dot product with itself = 1.

Length = 0.4^2 + 0.8^2 + c^2 =1
c = sqrt(1-(0.4^2+0.8^2)) = sqrt(0.2)

So it is answer a).

The magnitude must be 1
so 0.4^2 + 0.8^2 + c^2 =1
0.16 + 0.64 +c^2 =1
c^2 = 0.2
so a) √0.2 is the answer