Class 12 RD Sharma Solutions – Chapter 23 Algebra of Vectors – Exercise 23.6 | Set 2
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:
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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,
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Unit vector is,
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Question 13: Show that the points A(), B(), C() are the vertices of a right-angled triangle.
Solution:
Let,
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The line segments are,
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The magnitudes of the sides are,
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As we can see that
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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,
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The mid-point of the line segment joining 2 vectors is given by:
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Question 15: Find the value of x for which x() is a unit vector.
Solution:
The magnitude of the given vector is,
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For it to be a unit vector,
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Question 16: If , and , find a unit vector parallel to .
Solution:
Given, , and
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Thus, the unit vector is,
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Question 17: If , and , find a vector of magnitude 6 units which is parallel to the vector .
Solution:
Given, , and
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Unit vector in that direction is,
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Given that the vector has a magnitude of 6,
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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,
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Unit vector is,
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Given that the vector has a magnitude of 5,
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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:
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Thus, the length of the median is,
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=> units
Last Updated :
28 Mar, 2021
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