Three vectors ā, b̄, c̄ are coplanar iff their SCALAR TRIPLE PRODUCT [ā b̄ c̄] equals:
A|ā||b̄||c̄|
B0
C-1
D1
Answer & Solution
Correct answer: B. 0
Scalar triple product [ā b̄ c̄] = (ā × b̄)·c̄ = volume of parallelepiped. If volume is zero, vectors are coplanar (lie in same plane). So [ā b̄ c̄] = 0 ⟺ coplanar.
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: