Playbook
Vectors
228 q - 4.81/paper - 55% HARD. The largest chapter in the bank and the hardest of the cornerstones. Scalar Triple Product (71 q, 72% HARD) and Cross Product (66 q, 64%) carry 74% of its HARD between them, so this chapter DOES cherry-pick: secure Dot Product (50 q, 28% HARD) first.
- Questions in the bank
- 228
- q/paper (2024–25 shifts)
- 4.81
- Tagged HARD
- 55%
- Subtopics
- 6
Strand: Cornerstone
When you’ll see it
Quantities with direction: a dot or cross product, an area, a volume, a coplanarity test, or a geometry statement (median, centroid, parallelogram) posed in position vectors.
How this chapter is tested
228 q makes Vectors the largest chapter in the bank and 55% HARD makes it the hardest of the six cornerstones. Unlike Line and Plane, though, this chapter DOES cherry-pick, and that changes how you attack it. Scalar Triple Product (71 q, 72% HARD) and Cross Product (66 q, 64%) carry 74% of the chapter's HARD between them. Dot Product is 50 q at 28% HARD — a fifth of the chapter's volume at half the difficulty rate.
So the order is not negotiable: secure Dot Product first. It is the cheapest large block, it is where perpendicularity lives, and it is the prerequisite for reading a cross-product question correctly. Then Cross Product, then the Scalar Triple Product last, when you have the machinery to see it as a determinant rather than a formula to memorise.
The triple product is worth singling out because it is the chapter's real workhorse idea. A vanishing 3x3 determinant is a universal degeneracy test that surfaces in five or six chapters — as coplanarity here, as coplanarity of lines in Line and Plane, as collinearity of points, and as concurrency of lines in 2-D. Learning it once in vector form pays four times.
MHT-CET has no negative marking, and Vectors is where that matters most. A perpendicularity claim can be checked by taking one dot product per option; a coplanarity claim can be checked by evaluating one determinant. When the clock is short, verifying the four options is often faster than solving the stem — and there is no cost to a wrong guess.
The sub-skills
The distinct skills inside the chapter, in the order to learn them.
Magnitude, components, and unit vectors
Resolve into components, take a magnitude, and normalise. 10 q at 30% HARD — small, but every other subtopic assumes it and the normalisation step is where careless marks go.
Dot product, angle, and perpendicularity
The scalar product gives an angle, a projection, and the perpendicularity test (dot product zero). 50 q at 28% HARD: the cheap third of the chapter and the block to bank first.
Vector geometry — section formula, triangle, and parallelogram
Position vectors for midpoints, medians, centroids and diagonals. 16 q at 50% HARD. Mostly a translation skill: turn a geometry sentence into a vector equation, then the algebra is short.
Cross product, angle, and area
The vector product gives a perpendicular direction, a sine, and an area. Triangle area is HALF the cross-product magnitude; parallelogram area is the whole of it. 66 q at 64% HARD.
Linear combinations, collinearity, and coplanarity
Express one vector in terms of others and read off dependence. Three points are collinear when two of their joining vectors are parallel. 15 q at 53% HARD, and it is the conceptual bridge into the triple product.
Scalar triple product, coplanarity, and volume
One determinant answers three questions: the volume of a parallelepiped, one sixth of it for a tetrahedron, and coplanarity when it vanishes. 71 q at 72% HARD — the largest and hardest subtopic in the chapter, and the last one to learn.
Traps to expect
Distractor shapes this chapter reuses. The Traps page covers the patterns that cut across chapters.
Scalar answer offered for a vector question
A dot product is a number and a cross product is a vector. Options that mix the two types are the fastest elimination on the paper — check the type of the answer before you compute anything.
Triangle area without the half
The cross-product magnitude is the parallelogram area. The distractor is exactly double the correct triangle area, and it is present in nearly every area question.
Signed triple product taken as a volume
The scalar triple product carries a sign that depends on the ordering of the vectors. Volume is its modulus, so the negative of the right answer sits in the option list.
Coplanarity confused with parallelism
Triple product zero means the three vectors lie in one plane, not that any two of them point the same way. The trap option asserts a parallelism condition instead.
Learn it before you drill it
This chapter has full teaching notes — foundations, worked examples, self-checks and a per-subtopic mastery checkpoint. Read the notes once, then drill subtopic by subtopic below.
Vectors notesDrill every vectors question
228 questions from the bank, scoped to 6 bundled subtopics.
Drill one subtopic at a time
The 6 subtopics this playbook covers, in catalog order.
Related playbooks
Often paired with this one — the technique, the trap or the taxonomy overlaps. Drill these next.