Question

Compute the dot product of the vectors u and v​, and find the angle between the vectors. Bold v equals 7 Bold i minus Bold j and Bold w equals negative Bold i plus 7 Bold j Bold v times Bold w ​= negative 14 ​(Simplify your​ answer.) Find the magnitude of the vectors. StartAbsoluteValue Bold v EndAbsoluteValueequals StartRoot 50 EndRoot and StartAbsoluteValue Bold w EndAbsoluteValueequals StartRoot 50 EndRoot ​(Type exact​ answers, using radicals as​ needed.) The angle between the vectors is nothingdegrees. ​(Type your answer in degrees. Do not round until the final answer. Then round to the nearest tenth as​ needed.)

Answer 1

Answer:

$\theta = 106.3 degree$

Explanation:

As we know that

$\vec w = -\hat i + 7\hat j$

$\vec v = 7\hat i - \hat j$

also we know that

$\vec v. \vec w = -14$

it is given as

$\vec v. \vec w = (-\hat i + 7\hat j).(7\hat i - \hat j)$

$\vec v. \vec w = - 7 - 7 = -14$

also we can find the magnitude of two vectors as

$|v| = \sqrt{(-1)^2 + (7)^2}$

$|v| = \sqrt{50}$

similarly we have

$|w| = \sqrt{(7^2) + (-1)^2}$

$|w| = \sqrt{50}$

now we know the formula of dot product as

$\vec v. \vec w = |v||w| cos\theta$

$-14 = (\sqrt{50})^2cos\theta$

$\theta = cos^{-1}(\frac{-14}{50})$

$\theta = 106.3 degree$