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Class 12 RD Sharma Solutions – Chapter 23 Algebra of Vectors – Exercise 23.6 | Set 2
• Last Updated : 28 Mar, 2021

### Question 11: Find the position vector of the mid-point of the vector joining the points P( ) and Q( ).

Solution:

The mid-point of the line segment joining 2 vectors is given by:

=> => => => ### Question 12: Find the unit vector in the direction of the vector , where P and Q are the points (1,2,3) and (4,5,6).

Solution:

Let,

=> => => => => Unit vector is,

=> => => => ### Question 13: Show that the points A( ), B( ), C( ) are the vertices of a right-angled triangle.

Solution:

Let,

=> => => The line segments are,

=> => => => => => => => => The magnitudes of the sides are,

=> => => As we can see that => Thus, ABC is a right-angled triangle.

### Question 14: Find the position vector of the mid-point of the vector joining the points P(2, 3, 4) and Q(4, 1, -2).

Solution:

Let,

=> => The mid-point of the line segment joining 2 vectors is given by:

=> => => => ### Question 15: Find the value of x for which x( ) is a unit vector.

Solution:

The magnitude of the given vector is,

=> => => For it to be a unit vector,

=> => => ### Question 16: If , and , find a unit vector parallel to .

Solution:

Given,  and => => Thus, the unit vector is,

=> => => ### Question 17: If , and , find a vector of magnitude 6 units which is parallel to the vector .

Solution:

Given,  and => => Unit vector in that direction is,

=> => => Given that the vector has a magnitude of 6,

=> Required vectors are : = ### Question 18: Find a vector of magnitude 5 units parallel to the resultant of the vector and .

Solution:

Given, and The resultant vector will be given by,

=> => => Unit vector is,

=> => => Given that the vector has a magnitude of 5,

=> Required vectors are: ### Question 19: The two vectors and represent the sides and respectively of the triangle ABC. Find the length of the median through A.

Solution:

Let D be the point on BC, on which the median through A touches.

D is also the mid-point of BC.

The median is thus given by:

=> => => => => => Thus, the length of the median is,

=> => => units

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