Question

In: Computer Science

What is the angle between the following vectors a= 4i+3j+2k and I+2j+5k?

Expert Solution

What is the angle between the vectors

a= 4i+3j+2k

and

b=i +2j+5k

To find the angle we need to find the dot product

dot product = 4x1 + 3x2 + 2x5 = 4 + 6 + 10= 20

Next we need to calculate the magnitudes of the vectors

For a

sqrt (4^2 + 3^2 + 2^2) = sqrt (16 + 9 + 4)

=sqrt 29

For b

sqrt ( 1^2 + 2^2 + 5^2 ) = sqrt ( 1 + 4 + 25 )=sqrt 30

So we use the formula

Cos C = dot product/ magnitudes multiplied together

= 20/ ( sqrt29) (sqrt30)

= 20 / ( 5.385 x 5. 477 )

= 20 / 29.49

= 0.6782

Hence C = 47.29 degrees

angle=47.3°

Nipun Maity answered 2 years ago

How do I find the angle between two three-dimensional vectors?

If the angle between two vectors is 180 degrees, are the two vectors parallel?

Suppose that vectors x and y are such that IxI=3 and IyI=4, and the angle between...

Suppose that vectors x and y are such that IxI=3 and IyI=4, and the angle between x and y is 71°. Solve the triangle determined by the vectors 3x , y, and I3x - y I. That is, report all side lengths and angles in this triangle to 3 decimal places accuracy.

Find the angle θ between the vectors in radians and in degrees. u = cos π...

Find the angle θ between the vectors in radians and in degrees. u = cos π 3 i + sin π 3 j, v = cos 3π 4 i + sin 3π 4 j (a) radians (b) degrees

Calculate the angle between the vectors u = {5, -2, 3} and v ={4,-5,7}

Calculate the angle between the vectors u = {5, -2, 3} and v ={4,-5,7} give details.

1. a. Determine the angle (in radians) between the vectors 〈4, −5, 6〉 and 〈−2, 2,...

1. a. Determine the angle (in radians) between the vectors 〈4, −5, 6〉 and 〈−2, 2, 3〉. b. Find the vector projection of 〈1, 2, 4〉 onto 〈1, 1, 1〉. c. Compute the cross product 〈2, 3, 4〉 × 〈1, 0, −1〉.

Rewrite the following vectors in terms of their magnitude and angle (counterclockwise from the +x direction)....

Rewrite the following vectors in terms of their magnitude and angle (counterclockwise from the +x direction). (a) A displacement vector with an x component of +9.1 m and a y component of -9.5 m. magnitude angle (b) A velocity vector with an x component of -98 m/s and a y component of +38 m/s. magnitude angle (c) A force vector with a magnitude of 54 lb that is in the third quadrant with an x component whose magnitude is...

What is the difference between the Brewster angle and the critical angle?

1) Determine the angle between vectors: U = <2, -3, 4> and V= <-1, 3, -2>...

1) Determine the angle between vectors: U = <2, -3, 4> and V= <-1, 3, -2> 2) determine the distance between line and point P: -2x+3y-4z =2 L: 3x – 5y+z =1 3) Determine the distance between the line L and the point A given by L; (x-1)/2 = (y+2)/5 = (z-3)/4 and A (1, -1,1) 4) Find an equation of the line given by the points A, B and C. A (2, -1,0), B (-2,4,-1) and C ( 3,-4,1)...

Find the angle between each of the following pairs of vectors A⃗ =Axi^+Ayj^A→=Axi^+Ayj^ and B⃗ =Bxi^+Byj^B→=Bxi^+Byj^....

Find the angle between each of the following pairs of vectors A⃗ =Axi^+Ayj^A→=Axi^+Ayj^ and B⃗ =Bxi^+Byj^B→=Bxi^+Byj^. Ax1=Ax1= -1.00, Ay1=Ay1= 5.80; Bx1=Bx1= 1.00, By1=By1= -2.30. Ax2=Ax2= 3.60, Ay2=Ay2= 5.40; Bx2=Bx2= 11.0, By2=By2= 5.60. Ax3=Ax3= -4.00, Ay3=Ay3= 2.00; Bx3=Bx3= 7.00, By3=By3= 14.00.