Yes, the speed of light is the same in all directions in a vacuum. According to the theory of special relativity, which has been extensively supported by experimental evidence, the speed of light in a vacuum is considered to be a fundamental constant of nature. It is independent of the motion of the source of light or the observer measuring its speed.
This principle is known as the isotropy of the speed of light, which means that the speed of light is the same in all directions relative to any observer in a vacuum. Regardless of whether the observer is stationary or in motion, they will always measure the speed of light to be approximately 299,792,458 meters per second (or about 186,282 miles per second) in a vacuum.
It's important to note that the speed of light may appear different when measured in a medium other than a vacuum due to interactions with the material. In those cases, the speed of light can depend on factors such as the refractive index of the medium and the angle at which the light is traveling. However, in a vacuum, the speed of light is constant and does not vary with direction.