Question

Given the displacement vector
`D=3i-4j` find the displacement vector R so that
`D+R=-4Dj`

Answer 1

R = -3i + 4j + 12k

Step-by-step explanation:

Given that the displacement vector D is:

D = 3i - 4j

Substitute D in -4Dj to get the below vector

-4jD = -4j( 3i - 4j )

Using a cross product since the displacement are not parallel to each other

-4jD = (-4j × 3i) - ( -4j × 4j )

But j × I = - k while j × j = 0

-4jD = 12k

To find the displacement vector R,

Make R the subject of the formula in the equation below

D + R = 12k

(3i - 4j) + R = 12k

Use addition of vector

R = (- 3i + 4j + 0k) + ( 0i + 0j + 12k)

R = -3i + 4j + 12k

Answer 2

-3i+3j+16

Step-by-step explanation:

Given the displacement vector D = 3i-4j,, we are to find the displacement vector R so that D+R = -4Dj ..... 1

Substitute D = 3i+4j into equation1 as shown;

D+R = -4Dj

3i-4j + R = -4(3i-4j)j

R = -4(3i-4j)j - (3i-4j)

open the parenthesis

R = -4[(3(i.j)-(4j.j)] - (3i-4j)

R = -4[3(0)-4(1)]-3i+3j

R = -4(0-4)-3i+3j

R = 16-3i+3j

R = -3i+3j+16

Hence the displacement vector R so that D+R = -4Dj is -3i+3j+16