### Video Transcript

If vector π is equal to nine π’
minus seven π£ plus eight π€ and vector π is equal to eight π’ minus three π£ plus
four π€, find vector π minus two-thirds of vector π.

In this question, we will need to
recall how to subtract vectors and also how to multiply a vector by a scalar. Letβs begin by calculating
two-thirds of vector π.

In order to multiply any vector by
a scalar, we simply multiply each of the components by that scalar. Two-thirds multiplied by eight is
equal to sixteen-thirds. Therefore, two-thirds multiplied by
eight π’ is sixteen-thirds π’. Multiplying two-thirds by negative
three π£ gives us negative two π£. Finally, multiplying two-thirds by
four π€ gives us eight-thirds π€. Multiplying vector π by the scalar
two-thirds gives us sixteen-thirds π’ minus two π£ plus eight-thirds π€.

We need to subtract this vector
from vector π. In order to subtract two vectors,
we simply subtract the corresponding components. Nine π’ minus sixteen-thirds π’ is
equal to eleven-thirds π’. This is because nine can be
rewritten as twenty-seven thirds or 27 over three. Subtracting the π£-components gives
us negative five π£, as negative seven π£ minus negative two π£ is the same as
negative seven π£ plus two π£.

Finally, eight π€ minus
eight-thirds π€ is equal to sixteen-thirds π€. We know this as we can rewrite
eight as twenty-four thirds. And twenty-four thirds minus
eight-thirds is equal to sixteen-thirds. Vector π minus two-thirds of
vector π is therefore equal to eleven-thirds π’ minus five π£ plus sixteen-thirds
π€.