##\sqrt{2}## is the coefficient of the unit vector k.Yodaa said:Homework Statement
the angles which[/B] î + ĵ + √2k̂ makes with x axis, y-axis and z axis are?
The Attempt at a Solution
the question is basically asking us what angle î + ĵ + √2k̂ makes with î + ĵ + k̂ right?
So since √2 is just the magnitude i thought the answer would be 90, 90, 90
the answer given is 60, 60 and 45
PS: i just started learning vectors
The term "Angles Formed by Vector î + ĵ + √2k̂" refers to the measurement of the angle formed by the three-dimensional vector with components î, ĵ, and √2k̂.
The angles formed by Vector î + ĵ + √2k̂ can be calculated using the dot product formula: θ = arccos[(î·ĵ + ĵ·√2k̂ + √2k̂·î) / (|î| |ĵ| |√2k̂|)]. This formula gives the angle between two vectors, which can be applied to the three-dimensional vector in question.
The angles formed by Vector î + ĵ + √2k̂ are related to the x, y, and z components of the vector through the trigonometric functions sine, cosine, and tangent. For example, the angle formed by the x and y components can be calculated using the inverse tangent function: θ = arctan(y/x).
Yes, the angles formed by Vector î + ĵ + √2k̂ can be negative. This occurs when the vector is pointing in the opposite direction than the positive direction of the x, y, or z-axis, resulting in a negative angle measurement.
The angles formed by Vector î + ĵ + √2k̂ do not directly relate to the magnitude of the vector. However, the magnitude of the vector can be calculated using the Pythagorean theorem and the angles formed by the vector, as the magnitude is equal to the square root of the sum of the squares of the vector's components.