68 free MCQs on Vector Algebra, each with its own worked answer and explanation. Vectors, dot product, cross product, and geometric applications
Take the timed Vector Algebra chapterwise test →68 practice questions on Vector Algebra, sorted Easy → Hard. Try each one first, then open its answer page for the worked explanation. Want the full theory first? Read the Vector Algebra notes.
Triangle law of vector addition: placing vector b at the head of vector a, the diagonal from the start to the final head gives the resultant a + b.
Q1.
A quantity that has both magnitude and direction is called a:
Q3.
A unit vector has magnitude equal to:
Q4.
The unit vector along vector a is:
Q5.
Two vectors are equal if they have the same:
Q7.
If a = 2i - 3j + k and b = i + j - 2k, then a + b =
Q10.
If a . b = 0 and neither a nor b is zero, then a and b are:
Q11.
The cross product i x i equals:
Q13.
The position vector of point P(3, -2, 5) from the origin is:
Q14.
Scalar multiplication: if k = 3 and a = 2i - j, then ka =
Q15.
Collinear vectors are vectors that:
Q17.
The dot product formula a.b = |a||b|cos(theta). If theta = 0, then a.b =
Q18.
The triangle law of vector addition states that the third side of a triangle represents:
Q19.
A vector whose initial and terminal points are the same is called a:
Q20.
The parallelogram law of vector addition: |a + b|<sup>2</sup> + |a - b|<sup>2</sup> =
Q22.
The angle between a = i + j and b = j + k satisfies:
Q23.
If theta = 90 degrees and |a| = 3, |b| = 4, then |a x b| =
Q24.
The cross product satisfies:
Q25.
The scalar projection of vector a onto vector b is:
Q26.
The area of a parallelogram with adjacent sides a and b is:
Q27.
If a = i + j + k, the unit vector in the direction of a is:
Q28.
Three vectors a, b, c are coplanar if and only if:
Q29.
If a x b = 0 and both a and b are non-zero, then:
Q30.
The section formula: point dividing AB in ratio m:n internally (position vectors a, b) has position vector:
Q31.
The scalar triple product a.(b x c) gives:
Q32.
The vector component of a perpendicular to b is:
Q34.
Work done by force F over displacement d is:
Q35.
If a + b + c = 0, then a.b + b.c + c.a =
Q36.
The resultant of two equal vectors of magnitude F at angle theta has magnitude:
Q37.
The vectors |a| = 3, |b| = 2, a.b = 4. The angle theta satisfies:
Q38.
The midpoint of segment joining A(a) and B(b) has position vector:
Q39.
The moment (torque) of force F about a point is:
Q40.
If a.b = a.c and a is non-zero, it necessarily means:
Q41.
The vector triple product a x (b x c) equals (BAC-CAB rule):
Q42.
If |a + b| = |a - b|, then a and b must be:
Q43.
The scalar triple product satisfies:
Q44.
The area of triangle with vertices A(1,0,0), B(0,1,0), C(0,0,1) is:
Q45.
The identity (a x b).(c x d) equals:
Q46.
If a, b, c are mutually perpendicular unit vectors, |a + b + c|<sup>2</sup> =
Q47.
The volume of the tetrahedron with one vertex at origin, others at a, b, c is:
Q48.
The Lagrange identity states |a x b|<sup>2</sup> =
Q50.
If a x b = a x c (a is non-zero), then necessarily:
Q51.
For non-coplanar vectors a, b, c forming a basis, every vector r has a:
Q52.
In the reciprocal system, if a<sub>prime</sub> = (b x c)/[abc], then a . a<sub>prime</sub> =
Q53.
If ABCD is a parallelogram with diagonal AC = p and BD = q, then AB =
Q54.
The equation of a line through point a and perpendicular to both b and c is:
Q55.
Using a.b = |a||b|cos(theta): angle between a = 3i+4j and b = 4i+3j satisfies:
Q56.
If a = i+j, b = j+k, c = k+i, the scalar triple product [a b c] =
Q57.
The work done by F = 2i - j + k along displacement from A(1,0,0) to B(2,1,3) is:
Q58.
If vectors (2,-1,k), (1,2,-1), (0,1,2) are coplanar, then k =
Q59.
The vector equation of the plane through three points with position vectors a, b, c is:
Q61.
If a = i + j + k and b = i − j + k, the magnitude of a × b is:
Q62.
The projection of a = 2i + 3j + 2k on b = i + 2j + k is:
Q64.
The volume of the parallelepiped with edges i + j, j + k and k + i is:
Q65.
A unit vector perpendicular to both i + j and j + k is:
Q66.
If a, b, c are mutually perpendicular unit vectors, then |a + b + c| equals:
Q67.
The value of λ for which 2i + λj + k is perpendicular to i − 2j + 3k is:
Q68.
The area of the triangle with vertices A(1,1,1), B(2,3,5) and C(1,5,5) is:
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