Which of the following quantities are vectors.
All of them
1, 2, 5 and 6
3, 4
None of them
A vector has both magnitude and direction.
Which of the following are correct?
(1) cot(A+B) = cotAcotB−1cotA+cotB
(2) cot(A-B) = cotAcotB−1cotA−cotB
(3) tan(A+B) = tanA+tanB1−tanAtanB
(4) tan(A-B) = tanA−tanB1−tanAtanB
Let A = {1, 2, {3, 4}, 5}. Which of the following statements are incorrect and why?
(i) {3, 4} ⊂ A (ii) {3, 4} ∈ A
(iii) {{3, 4}} ⊂ A (iv) 1∈A
(v) 1⊂A (vi) {1, 2, 5} ⊂ A
(vii) {1, 2, 5} ∈ A (viii) {1, 2, 3} ⊂ A
(ix) Φ∈A (x) Φ⊂A
(xi) {Φ} ⊂ A.
Let A= {1, 2, {3, 4,}, 5}. Which of the following statements are incorrect and why?
(i) {3, 4}⊂ A
(ii) {3, 4}}∈ A
(iii) {{3, 4}}⊂ A
(iv) 1∈ A
(v) 1⊂ A
(vi) {1, 2, 5} ⊂ A
(vii) {1, 2, 5} ∈ A
(viii) {1, 2, 3} ⊂ A
(ix) Φ ∈ A
(x) Φ ⊂ A
(xi) {Φ} ⊂ A