Question

If a unit vector is represented by $ 0.5 \widehat{ i} - 0 . 8 \widehat{j} + c \widehat{k}$ then the value of c is

• A. $ \sqrt{ 0 . 0 1}$
• B. $ \sqrt{ 0 . 11}$
• C. 1
• D. $ \sqrt{ 0 . 39}$

Answer 1

The Correct Option is B

To determine the value of c, we need to use the fact that the given vector is a unit vector. A unit vector's magnitude is always 1. The given vector is 0.5 \widehat{i} - 0.8 \widehat{j} + c \widehat{k}.

The formula for the magnitude of a vector \vec{A} = a \widehat{i} + b \widehat{j} + c \widehat{k} is:

|\vec{A}| = \sqrt{a^2 + b^2 + c^2}

For a unit vector, |\vec{A}| = 1. Therefore,

\sqrt{(0.5)^2 + (-0.8)^2 + c^2} = 1

Squaring both sides gives us:

(0.5)^2 + (-0.8)^2 + c^2 = 1

Calculating the squares:

0.25 + 0.64 + c^2 = 1

Combining the constants:

0.89 + c^2 = 1

Subtract 0.89 from both sides to solve for c^2:

c^2 = 1 - 0.89 = 0.11

Take the square root of both sides to find c:

c = \sqrt{0.11}

Therefore, the value of c is \sqrt{0.11}, which matches the correct given option.