Question

2a + 5b - 3c - (4b - 3a + 6c) = …. a)5a + b - 9c b)5a - b - 9c c)5a + b + 9c d)5a - b + 9c

Answer 1

Step-by-step explanation:

We know that if these vectors are linearly dependent , then we can express one of them as a linear combination of the other two.  

Now let us assume that the given vector are coplanar, then we can write

5a+6b+7c=l(7a−8b+9c)+m(3a+20b+5c) where l and m are scalars

Comparing the coefficients of a,b and c

we get

7l+3m=5   .......(1)

−8l+20m=6    ......(2)

9l+5m=7   ......(3)

From equations (1) and (2) we get

20×(1)−3×(2)

140l+60m+24l−60m=100−18

⇒164l=82

⇒l=16482=21

Put l=21 in (1) we get

7l+3m=5

⇒3m=5−7l=

Answer 2

Answer:

a

Step-by-step explanation:

2a

$2a + 5b - 3c - (4b - 3a + 6c) = \\ 2a + 5b - 3c - 4b + 3a - 6c = \\ 2a + 3a + 5b - 4b - 3c - 6c = 5a + b - 9c$