Practicing the Intermediate 1st Year Maths 1A Textbook Solutions Inter 1st Year Maths 1A Addition of Vectors Solutions Exercise 4(b) will help students to clear their doubts quickly.

## Intermediate 1st Year Maths 1A Addition of Vectors Solutions Exercise 4(b)

I.

Question 1.
Find the vector equation of the line passing through the point $$2 \bar{i}+3 \bar{j}+\bar{k}$$ and parallel to the vector $$4 \bar{i}-2 \bar{j}+3 \bar{k}$$.
Solution: Question 2.
OABC is a parallelogram. If $$\overline{O A}=\bar{a}$$ and $$\overline{O C}=\bar{c}$$, find the vector equation of the side BC.
Solution:  Question 3.
If $$\overline{\mathbf{a}}, \overline{\mathbf{b}}, \overline{\mathbf{c}}$$ are the position vectors of the vertices A, B and C respectively of ∆ABC, theind the vector equation of the median through the vertex A.
Solution: Question 4.
Find the vertor equation of the line joining the points $$2 \bar{i}+\bar{j}+3 \bar{k}$$ and $$-4 \bar{i}+3 \bar{j}-\bar{k}$$.
Solution: Question 5.
Find the vector equation of the plane passing through the points $$\overline{\mathbf{i}}-2 \overline{\mathbf{j}}+5 \overline{\mathbf{k}},-5 \overline{\mathbf{j}}-\overline{\mathbf{k}} \text { and }-3 \overline{\mathbf{i}}+5 \overline{\mathbf{j}}$$.
Solution:  Question 6.
Find the vector equation of the plane through the points (0, 0, 0), (0, 5, 0) and (2, 0, 1).
Solution: II.

Question 1.
If $$\overline{\mathbf{a}}, \overline{\mathbf{b}}, \overline{\mathbf{c}}$$ are noncoplanar find the point of intersection of the line passing through the points $$2 \bar{a}+3 \bar{b}-\bar{c}$$, $$3 \bar{a}+4 \bar{b}-2 \bar{c}$$ with the line joining the points $$\bar{a}-2 \bar{b}+3 \bar{c}, \bar{a}-6 \bar{b}+6 \bar{c}$$.
Solution: Question 2.
ABCD is a trapezium in which AB and CD are parallel. Prove by vector methods, that the mid points of the sides AB, CD and the intersection of the diagonals are collinear.
Solution:    ⇒ M, P, N are collinear
Hence the midpoints of parallel sides of a trapezium and the point of intersection of the diagonals are collinear. Question 3.
In a quadrilateral ABCD, if the midpoints of one pair of opposite sides and the point of intersection of the diagonals are collinear, using vector methods, prove that the quadrilateral ABCD is a trapezium.
Solution:  III.

Question 1.
Find the vector equation of the plane which passes through the points $$2 \bar{i}+4 \bar{j}+2 \bar{k}, 2 \bar{i}+3 \bar{j}+5 \bar{k}$$ and parallel to the vector $$3 \overline{\mathbf{i}}-2 \overline{\mathbf{j}}+\overline{\mathbf{k}}$$. Also find the point where this plane meets the line joining the points $$2 \overline{\mathbf{i}}+\overline{\mathbf{j}}+3 \overline{\mathbf{k}}$$ and $$4 \bar{i}-2 \bar{j}+3 \bar{k}$$.
Solution:    Question 2.
Find the vector equation of the plane passing through points $$4 \overline{\mathbf{i}}-3 \overline{\mathbf{j}}-\overline{\mathbf{k}}$$, $$3 \overline{\mathbf{i}}+7 \overline{\mathbf{j}}-10 \overline{\mathbf{k}}$$ and $$2 \bar{i}+5 \bar{j}-7 \bar{k}$$, and show that the point $$\overline{\mathbf{i}}+2 \bar{j}-3 \overline{\mathbf{k}}$$ lies in the plane.
Solution:   