Write out the expression for [itex]\theta[/itex] in terms of the length of a x length of b and [itex]a_xb_x + a_yb_y + a_zb_z[/itex] (hint: you need the arccos function and pythagoras' theorem).jpd5184 said:Homework Statement
Use the definition of scalar product, a·b = ab cos θ, and the fact that a·b = axbx + ayby + azbz to calculate the angle between the two vectors given by a = 1.0 ihat + 5.0 jhat + 1.0 khat and b = 6.0 ihat + 3.0 jhat + 4.0 khat.
Homework Equations
a·b = ab cos θ
The Attempt at a Solution
i really don't have any clue were to start
To calculate the angle between two vectors, you can use the dot product formula: θ = cos^-1((a · b) / (|a| * |b|)), where a and b are the two vectors and |a| and |b| are the magnitudes of the vectors. Alternatively, you can use the cross product formula: θ = sin^-1(|a x b| / (|a| * |b|)).
No, the angle between two vectors cannot be negative. It is always measured in a counterclockwise direction and will always be between 0 and 180 degrees (or 0 and π radians).
The dot product of two vectors results in a scalar quantity, while the cross product results in a vector quantity. The dot product is used to calculate the angle between two vectors, while the cross product is used to determine the perpendicular vector to both of the original vectors.
No, the angle between two vectors cannot be greater than 180 degrees (or π radians). This is because the dot product formula for calculating the angle only gives values between 0 and 180 degrees. However, the cross product formula can give values greater than 180 degrees, but this represents the supplement angle (180 minus the calculated angle).
The angle between two vectors is affected by their direction. If the two vectors are in the same direction, the angle between them will be 0 degrees. If they are in opposite directions, the angle between them will be 180 degrees. If they are perpendicular to each other, the angle between them will be 90 degrees.