Question

please answer all of them; only need final answer

h. The length of the vector c = (2, -3, 1) is?

i. If |r| = 4, then the value of |-5r| is?

j. The cross product of vectors a = (-1, 4, 6) and b = (3, 0, 2) is?

k. The vectors v = (3, 4) is projected onto the x-axis The length of the projection is?

l. Rounded to the nearest integer, a two-dimensional vector with length 13 forming an angle of 67.4° with the x-axis has coordinates?

m. A three-dimensional unit vector parallel to the y-axis is?

Answer #1

(h)

Length of vector = |c| = sqrt (2^2 + (-3)^2 + 1^2) = sqrt 14 = 3.74

(i) Given |r| = 4, then

|-5r| = |-5|*|r| = 5*4 = 20

(j)

(k)

Length of projection of vector b onto a is: (a.b)/|a|

here b = (3, 4)

a = (1, 0) = unit vector on x-axis

So, (a.b) = (i).(3 i + 4 j) = 3*(i.i) + 4*(i.j) = 3*1 + 4*0

(a.b) = 3

|a| = 1, So

Length of projection = 3/1 = 3

(l)

x-component of vector, Rx = |R|*cos = 13*cos 67.4 deg = 4.9958

In nearest integer:

Rx = 5.0

y-component of vector, Ry = |R|*sin = 13*sin 67.4 deg = 12.0017

In nearest integer:

Ry = 12.0

Coordinates of Vector = (5.0, 12.0)

(m).

A three-dimensional unit vector parallel to the y-axis = 0 i + 1 j + 0 k = j

Vector = (0, 1, 0)

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