MP Board Class 12 (MPBSE) Vectors & 3D Geometry — practice questions
17 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice MP Board Class 12 (MPBSE) Vectors & 3D Geometry in the app →The distance between $(1, 2, 3)$ and $(4, 6, 3)$ in 3D is:The direction cosines of a line with direction ratios $(2, -1, 2)$ are:The plane $2x - y + 3z + 5 = 0$ has normal vector:The distance from $(1, 1, 1)$ to the plane $2x + 2y + z + 3 = 0$ is:The magnitude of the vector $\vec a = 3\hat i + 4\hat j$ is:The dot product $\vec a\cdot\vec b$ of $\vec a = 2\hat i - \hat j + 3\hat k$ and $\vec b = \hat i + 4\hat j + The cross product $\vec a\times\vec b$ of two parallel non-zero vectors is:Three vectors $\vec a, \vec b, \vec c$ are coplanar if and only if:If a = 2i + 3j + k and b = i − j + 2k, then a · b equals:Two non-zero vectors a and b are PERPENDICULAR if and only if:A UNIT VECTOR in the direction of v = 3i + 4j is:The scalar triple product [a b c] geometrically represents:The vector triple product a × (b × c) simplifies via:The Cartesian equation of a plane with intercepts 2, 3, 6 on the x, y, z axes is:For direction cosines l, m, n of any line in 3D:A point R divides the line joining P (position vector a) and Q (position vector b) INTERNALLY in the ratio m:nThe angle θ between two PLANES with normals n1 and n2 satisfies: