Vector Algebra

35 solved questions from Class 12 Mathematics, each with the full working. Tap any question to see the step-by-step solution.

• 1 What is the domain, range, or fundamental theorem introduced in 'Vector Algebra' (Class 12 Mathematics)? medium MCQ Functions & Theorems
• 2 What is the derivative or integral formula associated with 'Vector Algebra'? medium MCQ Calculus & Formulae
• 3 How do you find the solution set or optimum value in 'Vector Algebra'? medium MCQ Problem Solving & Optimization
• 4 Given a=2i+3j-k and b=-i+4j+2k, find the angle between them in degrees (nearest integer). medium 2 marks Angle between vectors
• 5 Find the magnitude of the vector u=3i-4j+12k. easy 1 mark Vector magnitude
• 6 Find the equation of the plane that passes through P(2,-1,3) and is perpendicular to the line x-14=(y+2)/-2=(z-0)/5. hard 3 marks Plane perpendicular to line
• 7 Find the vector projection of b onto a where a=2i+3j-k and b=-i+4j+2k. medium 2 marks Vector projection
• 8 Find the volume of the parallelepiped formed by the vectors a=(1,2,3), b=(4,-1,2) and c=(0,5,-1). medium 3 marks Scalar triple product (volume of parallelepiped)
• 9 Find the scalar (dot) product of vectors a= i+2j-3k and b=4i-j+k. easy MCQ 1 mark Scalar (dot) product
• 10 Find the perpendicular distance of the point Q(5,-2,1) from the line passing through A(1,0,2) and having direction ratios 2,-1,3. medium 2 marks Distance of a point from a line
• 11 Determine the equation of the plane that passes through the point (3,-1,2) and contains the line of intersection of the planes 2x - y + z = 5 and x + y - 4z = -2. hard 4 marks Plane through line of intersection of two planes
• 12 If a=i and b=i+j, the angle between a and b is: medium MCQ 2 marks Angle between two vectors
• 13 The points O(0,0,0), A(2,1,3), B(1,4,2) and C(3,2,5) are the vertices of a tetrahedron. Find its volume. (Give your answer in cubic units.) hard 5 marks Scalar triple product and volume of a tetrahedron
• 14 Find the magnitude of the vector u=5i-12j+0k. easy 1 mark Magnitude of a vector
• 15 Find the scalar (dot) product of vectors a=2i-j+4k and b=-3i+5j+k. medium 2 marks Scalar (dot) product
• 16 Find the volume of the parallelepiped formed by vectors a=(2,3,5), b=(-1,4,0) and c=(0,-2,3). hard 4 marks Scalar triple product (volume of parallelepiped)
• 17 Find the magnitude of the vector v=3i+4j-12k. easy MCQ 1 mark Magnitude of a 3‑D vector
• 18 Find the angle (in degrees) between vectors a=5i-2j+k and b=-3i+4j+7k. medium 2 marks Angle between two vectors using dot product
• 19 Find the equation of the plane that passes through point P(1,2,3) and is perpendicular to the line (x-4)/2=(y+1)/-3=z/5. hard 4 marks Plane perpendicular to a line (normal vector)
• 20 What is the magnitude of the vector v = 7i -24j? easy MCQ 3 marks Magnitude of a vector
• 21 Find the volume of the parallelepiped determined by a=(1,0,2), b=(0,3,1) and c=(2,1,0). hard 4 marks Scalar triple product and volume
• 22 Calculate the dot product of a = 2i +3j +4k and b = -i +5j. medium 3 marks Dot product of vectors
• 23 Determine the vector projection of b=(4,6,-2) onto a=(3,-1,2). hard 4 marks Vector projection
• 24 Find the magnitude of the vector v = 5i + 12j - 9k. easy 1 mark Magnitude of a 3‑D vector
• 25 Find the dot product of a = 3i - 4j + 2k and b = -i + 7j - 5k. medium 2 marks Dot product of two vectors
• 26 Find the volume of the parallelepiped formed by the vectors a=(3,-2,5), b=(1,4,-1), and c=(-2,3,0). hard 4 marks Volume via scalar triple product
• 27 Determine the equation of the plane that passes through the point P(2,3,-1) and contains the line of intersection of the planes 2x - y + 3z = 4 and x + 2y - z = 1. hard 5 marks Equation of a plane through a point and a line of intersection
• 28 Determine the volume of the parallelepiped formed by the vectors a=(1,2,3), b=(4,0,-1), and c=(2,-3,5). hard 5 marks Triple scalar product
• 29 Find the magnitude of the vector v=3i+4j+12k. easy 1 mark Magnitude of a vector
• 30 Find the vector projection of b=(4,-5,2) onto a=(3,1,0). medium 3 marks Vector projection
• 31 What is the angle (in degrees) between the vectors a=2i+3j+4k and b=5i-6j+2k? medium MCQ 2 marks Angle between vectors
• 32 Calculate the magnitude of the vector (mathbf{v}=(3,,-4,,12)). medium 2 marks magnitude of vector
• 33 Which of the following is the dot product of (mathbf{a}=(2,,-3,,5)) and (mathbf{b}=(-4,,1,,2))? easy MCQ 1 mark dot product
• 34 Find the volume of the parallelepiped formed by (mathbf{a}=(1,,2,,3)), (mathbf{b}=(0,,-2,,1)) and (mathbf{c}=(4,,1,,-1)). hard 4 marks scalar triple product
• 35 Determine the equation of the plane that passes through (P(2,,-1,,3)) and contains the line of intersection of (3x-2y+z=4) and (x+y+z=1). medium 3 marks plane through point containing line of intersection