Question $11$

$1$ point

How Did I Do$?$

Consider a plane which is parallel to two vectors vec$(u)=(-9,2,6)$ and vec$(v)=(6,7,7),$ and which contains the point $P=(-2,-1,2).$

a$)$ Are any two vectors parallel to the plane $($and a point on the plane$)$ enough to determine the equation of a plane?

Answer:

True

False

b$)$ If you answered false to the previous question, which condition must be satisfied by the two vectors? If you answered true to the previous question, just tick the box for Not applicable.

Not applicable

The two vectors must be linearly independent

The two vectors must point in opposite directions.

The two vectors must be orthogonal.

The two vectors must not contain the given point $P$ in the plan.

The two vectors must point in the same direction.

c$)$ Give a parametric equation of this plane, uisng $s$ and $t$ as the parameters.

Answer: $(x,y,z)=$

FORMATTING: Give your answer in the format $(x,y,z),$ where $x,y$ and $z$ are each functions of $s$ and $t.$ Warning: for this question, you must use strict calculator notations; in particular, you must use $*$ for every multipliaction $($e$.$g$.2t$ is written $2^{**}$ t$.)$

Question $11$

$1$ point

How Did I Do$?$

Consider a plane which is parallel to two vectors vec$(u)=(-9,2,6)$ and vec$(v)=(6,7,7),$ and which contains the point $P=(-2,-1,2).$

a$)$ Are any two vectors parallel to the plane $($and a point on the plane$)$ enough to determine the equation of a plane?

Answer:

True

False

b$)$ If you answered false to the previous question, which condition must be satisfied by the two vectors? If you answered true to the previous question, just tick the box for Not applicable.

Not applicable

The two vectors must be linearly independent

The two vectors must point in opposite directions.

The two vectors must be orthogonal.

The two vectors must not contain the given point $P$ in the plan.

The two vectors must point in the same direction.

c$)$ Give a parametric equation of this plane, uisng $s$ and $t$ as the parameters.

Answer: $(x,y,z)=$

FORMATTING: Give your answer in the format $(x,y,z),$ where $x,y$ and $z$ are each functions of $s$ and $t.$ Warning: for this question, you must use strict calculator notations; in particular, you must use $*$ for every multipliaction $($e$.$g$.2t$ is written $2^{**}$ t$.)$