Bihar Board Class 12 (Commerce) Vectors — practice questions
80 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice Bihar Board Class 12 (Commerce) Vectors in the app →Vectors that share the same initial point are called?Which term describes vectors that all end at the same terminal point?Two vectors are equal when they have the same?Vectors lying along or parallel to the same line are called?A vector that can be shifted anywhere in space without changing its magnitude or direction is a?A force applied only at one fixed point, such as on one stationary car, is an example of which vector type?Vectors that lie in the same plane or in parallel planes are called?The position vector of the point P(x, y, z) with respect to the origin is?What is the magnitude of the position vector of the point P(1, 4, 8)?What is the unit vector along the vector 2i - 2j + k?Which standard unit vector lies along the positive Y-axis?For a negative scalar k, the vector ka compared with a has?If |a| = 4 and k = -3, what is the magnitude of ka?Two non-zero vectors a and b are collinear when?Which vector is collinear with 2i - 3j + 6k?The negative of a vector has the same magnitude and what direction?Two forces acting at once on a body are combined using which law of vector addition?If xi + 3j equals 2i + yj, what is x + y?A vector r coplanar with non-collinear vectors a and b can be written uniquely as?Any vector in space is uniquely a linear combination of a, b, c when these three are?If xa + yb + zc = 0 forces x = y = z = 0, the vectors a, b, c are?Points with position vectors a, b, c are collinear iff xa + yb + zc = 0 for nonzero scalars with?By the section formula, the point dividing A(a) and B(b) internally in the ratio m:n is?The position vector of the midpoint of A(a) and B(b) is?Find the midpoint of the segment joining L(7, 6, 12) and N(5, 4, 2).The centroid of a tetrahedron with vertices a, b, c, d has position vector?In what ratio does the centroid of a triangle divide each median, from the vertex?The scalar product a . b of two non-zero vectors equals?For two non-zero perpendicular vectors, the dot product is?The dot product of a vector with itself, a . a, equals?Find a . b for a = i + 2j + 3k and b = 4i - 5j + 6k.What is the angle between the vectors i + j and j?For what value of m are 2i + mj + k and i - 2j + 4k perpendicular?The scalar projection of b on a is given by?Find the scalar projection of 2i + j + 5k on 3i + 4j.What are the direction cosines of the vector 6i + 2j + 3k?The cosines of the angles a vector makes with the coordinate axes are called its?The vector a x b is directed how relative to the plane of a and b?The vector product is anticommutative, which means b x a equals?If |a| = 3, |b| = 4 and the angle between them is 30 degrees, what is |a x b|?Since i, j, k form a right handed triplet, what is i x j?The area of a parallelogram with adjacent sides a and b equals?A cyclic change of a, b, c in a scalar triple product does what to its value?If [a b c] = 5, what is [b a c]?If three vectors are coplanar, their scalar triple product is?The volume of a parallelepiped with co-terminus edges a, b, c is?Find the volume of the parallelepiped with edges i + j, j + k and k + i.The dot product of two non-zero perpendicular vectors is alwaysBy the right-hand rule, what is the cross product i × j?What is the value of i · i for the unit vector i?A is (1, 2, 3) and B is (4, 6, 8). The vector AB equalsAdjacent sides of a parallelogram are 3i and 4j. What is its area?Two sides of a triangle are the vectors 3i and 4j. Its area isFor any two vectors a and b, the vector b × a equalsTwo unit vectors make an angle of 60 degrees. Their dot product isIf the scalar triple product of three vectors is zero, the vectors areA parallelepiped has edges i, 2j and 3k. Its volume isWhat is the value of i · (j × k)?The scalar projection of 3i + 4j on the vector i isThe sum of the vectors 2i + 3j and i - j isThe angle between i + j + k and i - j + k has cosine equal toThe cross product (i + j) × (j + k) equalsThe triple product expansion of a × (b × c) isAnother name for the dot product of two vectors is theWhich of these vector operations is commutative?A vector of magnitude 10 along 3i + 4j isA force 5i + j moves a body through 2i + 3j. The work done isA force of 3 N acts perpendicular to a lever arm of 2 m. The magnitude of its moment isTwo perpendicular vectors have magnitudes 6 and 8. Their resultant has magnitudeCompared with a, the vector -a hasThe midpoint of points with position vectors 2i + 4j and 6i + 8j has position vectorFor a unit vector with direction cosines l, m, n, the sum l² + m² + n² equalsThe direction cosine of i + j + k along the x-axis isA vector of magnitude 4 is multiplied by the scalar -3. The magnitude of the result isFor any vector a, the cross product a × a equalsThe vectors i + j and j + k are adjacent sides of a parallelogram. Its area isA tetrahedron has three mutually perpendicular edges i, j and k from one vertex. Its volume isIn vector analysis the magnetic field B is classed as aWho, with Heaviside, introduced the dot and cross notation for vector products in 1881?In physics, the acceleration of a point is the time derivative of its