Question

Let vector B = 5.35 m at 60°. Let vector C have the same magnitude as vector A and a direction angle greater than that of vector A by 25°. Let vector A · vector B = 30.6 m2 and vector B · vector C = 36.9 m2. Find the magnitude and direction of vector A .

Answer 1

Answer:

magnitude = 10.8

angle = 118 degree

Explanation:

Magnitude of vector B is 5.35 m and angle is 60 degree

so we have

$\vec B = 5.35 cos60\hat i + 5.35 sin60 \hat j$

$\vec B = 2.675 \hat i + 4.63 \hat j$

Now let the magnitude of vector A is "x" and it makes and angle theta

so we have

$\vec A = x cos\theta \hat i + x sin\theta \hat j$

now for vector C we have

$\vec C = x cos(\theta + 25) \hat i + x sin(\theta + 25)$

now we know that

$\vec A. \vec B = 2.675 x cos\theta + 4.63 x sin\theta$

$30.6 = x(2.675 cos\theta + 4.63 sin\theta)$

also we know that

$\vec B. \vec C = 2.675 x cos(\theta + 25) + 4.63 x sin(\theta + 25)$

$36.9 = x(2.675 cos(\theta + 25) + 4.63 sin(\theta + 25))$

now we have

$\theta = 118 degree$

$x = 10.8 m$