Raghav Gupta said:Homework Statement
Let a and b be two unit vectors such that | a + b| = √3. If
c = a+ 2b + 3(a x b), then 2|c| is equal to:
√55
√51
√43
√37
Homework Equations
a x b = |a| |b| sinθ n where n is a unit vector
## | a + b | = \sqrt{a^2 + b^2 + 2abcosθ} ##
The Attempt at a Solution
Found cosθ = 1/2 and θ = π/3
Then 3 a x b = 3√3/2 n
Now how to find c?
We don't know angle between n and a or n and b
I know angle is π/3Ray Vickson said:Yes, you do know the angle. Go back and review the definition and properties of axb.
Raghav Gupta said:I know angle is π/3
What to do next?
Raghav Gupta said:Oh that is 90°. But how I will evaluate c?
## |c|^2 = (a+2b)^2 + [3( a X b )]^2 + 2( a+2b)3( a X b ) cos θ ##Ray Vickson said:What is preventing you from writing out all the terms of |c|^2 and evaluating them one-by-one?
what does the dot product of the two yield?Raghav Gupta said:What is the angle between (a+ 2b) and a x b ?
Yes.Raghav Gupta said:It yields 0, so the angle is 90°?
Raghav Gupta said:## |c|^2 = (a+2b)^2 + [3( a X b )]^2 + 2( a+2b)3( a X b ) cos θ ##
What is the angle between (a+ 2b) and a x b ?
Between a and a x b it is 90°.
A vector is a mathematical quantity that has both magnitude (size) and direction. It is typically represented by an arrow pointing in the direction of the vector with its length representing the magnitude.
The magnitude of a vector is calculated using the Pythagorean theorem, which states that the magnitude is equal to the square root of the sum of the squares of the vector's components. In other words, you square the x-component of the vector, square the y-component, add the two values, and then take the square root of the result.
The units used to measure vector magnitude depend on the type of vector being measured. For example, velocity vectors are measured in meters per second, force vectors are measured in newtons, and electric field vectors are measured in volts per meter.
No, a vector's magnitude is always a positive value. However, the direction of the vector can be negative if it is pointing in the opposite direction of a positive reference axis.
When two vectors are added together, the resulting vector will have a magnitude that is equal to the sum of the magnitudes of the individual vectors. This means that vector addition can increase or decrease the magnitude of a vector depending on the direction and magnitude of the added vector.