Home › UP Board Class 12 › mathematics › Vectors & 3D Geometry › The scalar triple product [a b c] geometrically …
The scalar triple product [a b c] geometrically represents:
AThe angle between a and (b × c)
BThe unit normal to the plane of a, b, c
CThe sum of magnitudes a + b + c
DVolume of the parallelepiped with edges a, b, c
Answer & Solution
Correct answer: D. Volume of the parallelepiped with edges a, b, c
[a b c] = a · (b × c) = SIGNED VOLUME of the parallelepiped with edges a, b, c. If 0, the three vectors are COPLANAR.
Related questions
The angle θ between two PLANES with normals n1 and n2 satisfies:A point R divides the line joining P (position vector a) and Q (position vector b) INTERNAFor direction cosines l, m, n of any line in 3D:The Cartesian equation of a plane with intercepts 2, 3, 6 on the x, y, z axes is:The vector triple product a × (b × c) simplifies via:A UNIT VECTOR in the direction of v = 3i + 4j is:Two non-zero vectors a and b are PERPENDICULAR if and only if:If a = 2i + 3j + k and b = i − j + 2k, then a · b equals: