Find ā × b̄ where ā = î + 2ĵ + k̂ and b̄ = 2î + ĵ + 3k̂:
Aî + ĵ + k̂
B5î - ĵ + 5k̂
C5î - ĵ - 3k̂
D5î - 5ĵ - 5k̂
Answer & Solution
Correct answer: C. 5î - ĵ - 3k̂
Use determinant: ā × b̄ = |î ĵ k̂; 1 2 1; 2 1 3|. i: 2(3)-1(1) = 6-1 = 5 (positive). j: -(1×3 - 1×2) = -(3-2) = -1 (so coefficient -1). k: 1(1)-2(2) = 1-4 = -3 (so coefficient -3). Result: 5î - ĵ - 3k̂.
Related questions
Three vectors $\vec a, \vec b, \vec c$ are coplanar if and only if:The cross product $\vec a\times\vec b$ of two parallel non-zero vectors is:The dot product $\vec a\cdot\vec b$ of $\vec a = 2\hat i - \hat j + 3\hat k$ and $\vec b =The magnitude of the vector $\vec a = 3\hat i + 4\hat j$ is:The magnitude of the vector $\hat{i}+\hat{j}+\hat{k}$ is:For any vector $\vec a$, the dot product $\vec a\cdot\vec a$ equals:The value of $\hat{i}\times\hat{j}$ is:The dot product of $(2\hat{i}+3\hat{j}+\hat{k})$ and $(\hat{i}-\hat{j}+\hat{k})$ is: