Mathematics: Three vectors a, b, and c are related to one another such that 2a + 3b = 18c. a fourth vector d exists such that 6c + d = a. determine an expression for d in terms of the vectors a and b.

i havent yetStep-by-step explanation:...

Three vectors a, b, and c are related to one

Nicoleazaria

12.03.2022

we are given equations of vectors as

2a + 3b = 18c

6c + d = a

now, we want to find an expression for d in terms of the vectors a and b

so, we can eliminate c from second equation

so, we will solve for c from first equation

2a + 3b = 18c

divide both sides by 18

we get

$c=\frac{1}{9} a+\frac{1}{6} b$

now, we can plug this in second equation

$6(\frac{1}{9} a+\frac{1}{6} b) + d = a$

we can simplify it

$6*\frac{1}{9} a+6*\frac{1}{6} b + d = a$

$\frac{2}{3} a+ b + d = a$

$d = a-\frac{2}{3} a-b$

$d = \frac{1}{3} a-b$ ..............Answer

0,0(0 оценок)