Answer:

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The vector e can be represented as -12i - 24j

Given:

The magnitude of vector a = 10

The magnitude of vector b = 15

To Find:

A vector that satisfies the given conditions which is c

Solution:

Let the vector a be denoted as = 10i + 25j

Let the vector b be denoted as = 2i - j.

Let the vector c be = ci + dj.

Utilising vector addition to frame the equation -

a + b + c = 0

Substituting the values -

(10i + 25j) + (2i - j) + (ci + dj) = 0

Equating the coefficients separately -

Calculating for i component -

10 + 2 + c = 0

12 + c = 0

c = -12

Calculating for j component -

25 - 1 + d = 0

24 + d = 0

d = -24

Answer: The vector e can be represented as -12i - 24j.

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