Physics - Vectors Question with Solution | TestHub

Using Lagrange's identity:

$|\vec{a}\times \vec{b}{|}^2+(\vec{a}\cdot \vec{b}{)}^2=|\vec{a}{|}^2|\vec{b}{|}^2$

Substituting the given values:

$(35{)}^2+(\vec{a}\cdot \vec{b}{)}^2=(\sqrt{26}{)}^2(7{)}^2$

$1225+(\vec{a}\cdot \vec{b}{)}^2=26\times 49$

$1225+(\vec{a}\cdot \vec{b}{)}^2=1274$

$(\vec{a}\cdot \vec{b}{)}^2=1274-1225$

$(\vec{a}\cdot \vec{b}{)}^2=49$

$\vec{a}\cdot \vec{b}=7$

Answer: 7