0.4i + bj is a unit vector what is the value of b

October 21, 2026Mathematics

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Answer

\pm\sqrt{0.84}

3 steps

The value of $b$ is $\pm\sqrt{0.84}$ .

Understand the definition of a unit vector
A unit vector is a vector with a magnitude of 1. For a vector $\mathbf{v} = x\mathbf{i} + y\mathbf{j}$ , its magnitude is given by $|\mathbf{v}| = \sqrt{x^2 + y^2}$ .
Set up the equation for the magnitude
Given the vector $0.4\mathbf{i} + b\mathbf{j}$ , we have $x = 0.4$ and $y = b$ . Since it's a unit vector, its magnitude must be 1:
$\sqrt{(0.4)^2 + b^2} = 1$
Solve for $b$
Square both sides of the equation:
$(0.4)^2 + b^2 = 1^2$ $0.16 + b^2 = 1$
Subtract 0.16 from both sides:
$b^2 = 1 - 0.16$ $b^2 = 0.84$
Take the square root of both sides:
$b = \pm\sqrt{0.84}$ $b \approx \pm 0.9165$
The value of $b$ is:

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