NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra — Exercise 10.20

Question 1:Write down a unit vector in XY-plane, making an angle of 30° with the positive direction of x-axis.

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Question 2:Find the scalar components and magnitude of the vector joining the points P(x1 , y1 , z 1 ) and Q (x2 , y2 , z 2 ).

Question 3:A girl walks 4 km towards west, then she walks 3 km in a direction 30° east of north and stops. Determine the girl’s displacement from her initial point of departure.

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Question 4:If abc , then is it true that | || | | | ab c ? Justify your answer.

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Question 5:Find the value of x for which ˆ ˆ ˆ x( ) i jk is a unit vector.

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Question 6:Find a vector of magnitude 5 units, and parallel to the resultant of the vectors ˆˆ ˆˆ ˆ ˆ a i jk b i jk 2 3 and 2 .

Question 7:If ˆˆ ˆˆ ˆ ˆ ˆˆ ˆ ai jkb i j k ci jk , 2 3 and 2 , find a unit vector parallel to the vector 2 – 3 ab c .

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Question 8:Show that the points A (1, – 2, – 8), B(5, 0, –2) and C(11, 3, 7) are collinear, and find the ratio in which B divides AC.

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Question 9:Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are (2 ) and ( – 3 ) ab a b externally in the ratio 1 : 2. Also, show that P is the mid point of the line segment RQ.

Question 10:The two adjacent sides of a parallelogram are ˆˆ ˆˆ ˆ ˆ 2 4 5 and 2 3 i jk i jk . Find the unit vector parallel to its diagonal. Also, find its area.

Question 11:Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are 111 ,,. 333

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Question 12:Let ˆ ˆ ˆ ˆ ˆˆ ˆˆ ˆ a i j kb i j k c i j k 4 2 , 3 2 7 and 2 4 . Find a vector d which is perpendicular to both a b and , and c d 15 .

1. Write down a unit vector in XY-plane, making a

Question 13:The scalar product of the vector ˆ ˆ ˆ i jk with a unit vector along the sum of vectors ˆ ˆ ˆ 245 i jk and ˆ ˆ ˆ i jk 2 3 is equal to one. Find the value of .

Question 14:If a b , , c are mutually perpendicular vectors of equal magnitudes, show that the vector abc is equally inclined to ab c , and

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Question 15:Prove that 2 2 ( )( ) | | | | ab ab a b , if and only if a b, are perpendicular, given a b 0, 0 . Choose the correct answer in Exercises 16 to 19

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Question 16:If is the angle between two vectors a b and , then a b 0 only when (A) 0 2 (B) 0 2 (C) 0 < < (D) 0

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Question 17:Let a b and be two unit vectors and is the angle between them. Then a b is a unit vector if (A) 4 (B) 3 (C) 2 (D) 2 3

Question 18:The value of ˆˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ij k ji k ki j .( ) ( ) ( ) is (A) 0 (B) –1 (C) 1 (D) 3

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Question 19:If is the angle between any two vectors a b and , then | || | ab a b when is equal to (A) 0 (B) 4 (C) 2 (D)