alleryThree 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.**
Keep practising Unit 9A: Parametric Equations and Plane Curves
Browse all Unit 9A: Parametric Equations and Plane Curves questions for GRE, or explore more Mathematics topics.
Related questions
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:The unit vector in the direction of $3\hat{i} + 4\hat{j}$ is:Two non-zero vectors $\vec a$ and $\vec b$ are perpendicular if and only if:The magnitude of the cross product $|\vec{a}\times\vec{b}|$ equals:The value of $\hat{i}\cdot\hat{j}$ is: