If a vector is pointing northwest, what are the signs of its x and y components?

A vector in the second quadrant has components x = -12 units and y = 5 units. What is the magnitude of the vector?

A vector makes an angle of 60 degrees with the positive y-axis in the second quadrant. What is its reference angle relative to the x-axis?

A particle moving in the wind has a velocity of (17 i - 6j) mph that lasts for 45 min. The wind changes direction affecting the particle velocity. The new velocity is (5i + 18j) mph and lasts for 1.5 h. Calculate the displacement of the particle, giving the result in component form with unit vectors.

For vectors A = 3i + 4j + 5k; B = 4i + 2j + √5 k, what would be the ratio of the magnitude of A to B?

Use vectors M and N as given in the drawing below. Determine P = M + N, giving the result in component form with unit vectors.

A car is moving on a three-dimensional coordinate system, and its velocity is represented by the vector $\(\overrightarrow{V}\)$ = (25.0î + 10.0ĵ - 15.0k̂) m/s. Determine the angles that this velocity vector makes with the x, y, and z axes.

Vector $\(\overline{M}\)$ lies in the xy plane making an angle of θ above the positive x-axis. Vector $\(\overline{N}\)$ is lying in the same plane making an angle Φ below the positive x-axis. Determine their dot product.

Hint: Use one of the following identities-

cos(A + B) = cosAcosB - sinAsinB

cos(A - B) = cosAcosB + sinAsinB

Find the vector magnitude and direction of the vector product M x N for the two vectors below.

Find the magnitude of the cross product (E ✕ F ) of the given vectors.

A car moves eastward with a velocity of 50 km/h. Is this velocity a vector quantity and why?

In a physics experiment, you measure the temperature of a liquid as 25°C. Is this a vector or a scalar quantity and why?

Two vectors, 6 N north and 8 N east, are combined. What is the magnitude of the resultant vector?