Intersection points Quiz 1

Question 1

Choose the correct intersection point for the lines $$2x + 2y + 3 = 0$$ and $$3x + 2y + 5 = 0$$.

Accepted Answer

$$\left( - 2,\dfrac{1}{2}\right)$$

Answer

$$\left(2,\dfrac{1}{2}\right)$$

Answer

$$\left(2, - \dfrac{1}{2}\right)$$

Answer

$$\left( - 2, - \dfrac{1}{2}\right)$$

Question 2

Choose the correct equation of the plane which is passing through the intersection of two planes whose equation are $$2x + y + z = 1$$ and $$2x + 3y + 2z = 5$$ which is perpendicular to the other plane $$x - y + 2z = 0$$.

Accepted Answer

$$ - 2y - z + 4 = 0$$

Answer

$$ - 2x - y + 4 = 0$$

Answer

$$2y - z + 4 = 0$$

Answer

$$2y - z - 4 = 0$$

Question 3

Tick the correct equation of the plane which is passing through the intersection of the planes $$3x - 2y + 3z - 4 = 0$$ and $$x + y + z - 2 = 0$$ and the point is $$(2,2,1)$$.

Accepted Answer

$$8x - 7y + 8z - 10 = 0$$

Answer

$$8x + 7y + 8z - 10 = 0$$

Answer

$$ - 8x + 7y + 8z - 10 = 0$$

Answer

$$8x - 7y + 8z + 10 = 0$$

Question 4

Mark the point of intersection of pair of straight lines which is represented by the equation $$6{x^2} + 6xy - 21{y^2} + 14x + 38y - 5 = 0$$

Accepted Answer

$$\left( - \dfrac{{32}}{{23}},\dfrac{{17}}{{23}}\right)$$

Answer

$$\left(\dfrac{{32}}{{23}}, - \dfrac{{17}}{{23}}\right)$$

Answer

$$\left( - \dfrac{{32}}{{23}}, - \dfrac{{17}}{{23}}\right)$$

Answer

$$\left(\dfrac{{32}}{{23}},\dfrac{{17}}{{23}}\right)$$

Question 5

Mark the correct vector equation of plane which is passing through the intersection of planes given $$\mathop r\limits^ 	o  .(2\widehat i + 3\widehat j - 3\widehat k) = 7$$ and $$\mathop r\limits^ 	o  .(2\widehat i + 4\widehat j + 3\widehat k) = 9$$ through the point $$(2,2,3)$$.

Accepted Answer

$$\mathop r\limits^ 	o  .(3\widehat i + 4\widehat j - 9\widehat k) =  - 5$$

Answer

$$\mathop r\limits^ 	o  .(3\widehat i - 4\widehat j - 9\widehat k) =  - 5$$

Answer

$$\mathop r\limits^ 	o  .(34\widehat i - 60\widehat j - 3\widehat k) = 136$$

Answer

$$\mathop r\limits^ 	o  .(34\widehat i + 60\widehat j - 3\widehat k) = 136$$