Question

If the entries of two vectors $\overrightarrow{\mathbf{v}}$and $\overrightarrow{\mathbf{w}}$in ${\mathit{R}}^{\mathbf{n}}$are all positive, then $\overrightarrow{\mathbf{v}}$and $\overrightarrow{\mathbf{w}}$must enclose an acute angle.

Short answer

The given statement is true.

Step-by-step solution

Acute angle

An angle that is less than $\mathbf{90}\mathbf{°}$is called an acute angle.

check the statement

For example,

$75°,45°,30°$

All entries are positive, and their dot product will be positive,

So that,

$\overrightarrow{v}\overrightarrow{w}cos\theta$will also positive

Which implies that $cos\theta$is positive

Then $\theta$is an acute angle.

Hence, the given statement is true.