Vectors
- The area of the parallelogram whose diagonals are \(3\hat i+\hat j-2\hat k\) and \(\hat i-3\hat j+4\hat k\) is Answer: B. 5sqrt3 vec d₁×vec d₂=-2hat i-14hat j-10hat k , magnitude √(300)=10sqrt3 . Area =1/2|vec d₁×vec d₂|=5sqrt3 . 1
- The vectors \(\hat i+2\hat j+3\hat k\), \(2\hat i+\hat j+\lambda\hat k\) and \(3\hat i+\hat j+2\hat k\) are coplanar if \(\lambda=\) Answer: C. 9/5 beginvmatrix1&2&3\\2&1&λ\\3&1&2endvmatrix=(2-λ)-2(4-3λ)+3(2-3)=5λ-9=0 . 1
- If \(|\vec a|=2\), \(|\vec b|=3\) and \(|\vec a+\vec b|=\sqrt{19}\), the angle between \(\vec a\) and \(\vec b\) is Answer: B. π/3 19=4+9+2vec a·vec b⇒vec a·vec b=3=6cosθ⇒cosθ=1/2 . 1