1. Find | |, if 7 7 and 3 2 2 ab a i j k b i j k . 2. Find a unit vector perpendicular to each of the vector ab ab and , where a i j k bi j k 3 2 2 and 2 2 . 3. If a unit vector a makes angles with , with 3 4 i j and an acute angle with k , then find and hence, the components of a . 4. Show that ( )( ) ab ab = 2( ) a b 5. Find and if (2 6 27 ) ( ) 0 i j kijk . 6. Given that a b 0 and a b 0 . What can you conclude about the vectors a b and ? 7. Let the vectors ab c , , be given as 1 2 31 2 3 ai a j a k bi b j bk , , 12 3 ci c j c k . Then show that a b c ab ac ( ) . 8. If either a b 0 or 0, then a b 0 . Is the converse true? Justify your answer with an example. 9. Find the ar
Question 1:Find ˆˆ ˆˆ ˆ ˆ | |, if 7 7 and 3 2 2 ab a i j k b i j k .
Question 2:Find a unit vector perpendicular to each of the vector ab ab and , where ˆˆ ˆˆ ˆ ˆ a i j k bi j k 3 2 2 and 2 2 .
Question 3:If a unit vector a makes angles with , with ˆ ˆ 3 4 i j and an acute angle with ˆk , then find and hence, the components of a .
Question 4:Show that ( )( ) ab ab = 2( ) a b
Question 5:Find and ➭ if ˆ ˆ ˆˆ ˆ ˆ (2 6 27 ) ( ) 0 i j kijk .
Question 6:Given that a b✓ ✔ 0 and a b ✔ 0 . What can you conclude about the vectors a b and ?
Question 7:Let the vectors ab c , , be given as 1 2 31 2 3 ˆˆ ˆˆ ˆ ˆ ai a j a k bi b j bk , , 12 3 ˆ ˆ ˆ ci c j c k . Then show that a b c ab ac ( ) .
Question 8:If either a b 0 or 0, ✕ ✕ ✕ ✕ then a b ✔ 0 . Is the converse true? Justify your answer with an example.
Question 9:Find the area of the triangle with vertices A(1, 1, 2), B(2, 3, 5) and C(1,5,5)
Question 10:Find the area of the parallelogram whose adjacent sides are determined by the vectors ˆ ˆ ˆ ai j k 3 and ˆ ˆ ˆ b i jk 2 7 .
Question 11:Let the vectors a b and be such that 2 | | 3 and | | 3 a b , then a b is a unit vector, if the angle between a b and is (A) /6 (B) /4 (C) /3 (D) /2
Question 12:Area of a rectangle having vertices A, B, C and D with position vectors 1 1 ˆˆ ˆˆ ˆ ˆ – 4, 4 2 2 i j ki j k , 1 ˆ ˆ ˆ 4 2 i jk and 1 ˆ ˆ ˆ – 4 2 i jk , respectively is (A) 1 2 (B) 1 (C) 2 (D) 4
