Page 82 - Mathematics Class - XII

Case-Study Based Questions
Case-Study Based Questions
Vikrant purchased an air-plant holder which is in the shape of tetrahedron.
Let A, B, C and D are the coordinates of the air plant holder where
A ≡ (1, 1, 1), B ≡ (2, 1, 3), C ≡ (3, 2, 2), D ≡ (3, 3, 4)

Read the above information carefully and answer the following questions

1. Find the position vector of AB .

 
 
(a) −−i 2 k  (b) 2ik+ (c)  i + 2  (d) −−2ik
k

2. Find the position vector of AC



 
 
(a) 2i −− (b) 2i ++ (c) 2i   j k (d) i +   j k+ 2 
j k
j k

3. Find the position vector of AD .

 


(a) 2i −   j − 2 k 3 (b) i 3 (c) 3i +  2 j +  2k (d) 2i +  2 j +  3k

j
k
4. Area of ∆ ABC =
(a) 11 sq. units (b) 14 sq. units (c) 13 sq. units (d) 17 sq. units
2 2 2 2
Assertion-Reason Based Questions
Assertion-Reason Based Questions
Directions for Questions 1 to 3: In each of the questions given below, there are two statements marked as
Assertion (A) and Reason (R). Mark your answer as per the codes provided below:
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false. (d) A is false but R is true.
→
→
Q. 1. Assertion (A) : If a and b represents the adjacent vectors of a triangle then the area of triangle
→
→
is 1 | a × b |
2
→
→
Reason (R) : Area of ∆ ABC = 1 | a | | b | sin θ, where θ is the angle between the adjacent
2
→
→
vectors a and b .
→→ →
Q. 2. Assertion (A) : For any three vectors ab, and c then ab c b ca ca b

Reason (R) : Cyclic permutation of three vectors does not change the value of the scaler
triple product.



i . The angle
j
i
Q. 3. Assertion (A) : The adjacent sides of a parallelogram are along a 2 and b 2   j
between the diagonals is 150°.
Reason (R) : Two vectors are perpendicular to each other if their dot product is zero.
Answers
Case-Study Based Questions: 1. (c) 2. (b) 3. (d) 4. (b)
Assertion-Reason Based Questions: 1. (a) 2. (a) 3. (d)

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