CBSE Class 12 (Commerce) Vector Algebra — practice questions
91 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice CBSE Class 12 (Commerce) Vector Algebra in the app →Three vectors $\vec a, \vec b, \vec c$ are coplanar if and only if:A quantity with magnitude as well as direction is a:Which of these is a scalar quantity?Which of these is a vector quantity?A vector whose initial and terminal points coincide is the:A vector of magnitude one is called a:The distance between initial and terminal points is the vector's:On a vector diagram, direction is shown by the:The unit vector along a given vector is written with which symbol?Adding vectors by completing a parallelogram is the:Vector addition where order does not matter is called:The additive identity for vectors is the:The vectors i, j and k each have magnitude:The vectors i, j and k lie along which axes?A vector joining two points is found by applying the:A directed line segment has magnitude and:The girl's net movement from A to C is represented by a:Where does a vector start, in the standard naming?Multiplying a vector by a scalar changes its:Which quantity in this list is NOT a vector?A unit vector is mainly used to show a vector's:Multiplying a vector by a scalar gives a result that is:A vector multiplied by a scalar stays collinear with the:A negative scalar multiplier gives a vector whose direction is:The magnitude of a scaled vector equals the original magnitude times the scalar's:Writing a vector as x i plus y j plus z k gives its:The numbers x, y and z in component form are also called:The section formula concerns a segment PQ divided by a third point in how many ways?A point dividing PQ between P and Q divides it:A point dividing PQ beyond the segment divides it:The projection of a vector on a line is itself a:The magnitude of the projection uses the cosine of the angle with the:The direction of the projection depends on the sign of the:Projection of a vector on a line is the dot product with the line's:The scalar product obeys laws that are:The scalar product is an operation that is:The vector product is an operation that is:The angle between two vectors can be found in terms of their:The cross product of two nonzero vectors is zero when they are:For mutually perpendicular unit vectors, i cross j equals:The area of a parallelogram with sides a and b uses the magnitude of their:The area of a triangle from its three vertices can be found using:The result a cross b is a:Why does the notation |a| < 0 have no meaning for a vector a?A point P has coordinates (2, 3, 6). What is the magnitude of OP, with O the origin?Each direction cosine of the vector i + j + k equalsThe magnitude of a unit vector isTwo vectors are equal when they have the sameThe negative of a vector a has the same magnitude as a butTwo collinear vectors have equal magnitudes. Then they areIn triangle ABC, the vector AB plus the vector BC equals the vectorFor any two vectors a and b, the relation a + b = b + a shows that vector addition isThe rule (a + b) + c = a + (b + c) is the property of vector addition calledThe additive inverse of a vector a isIf the magnitude of a is 4, the magnitude of −3a isThe vectors i, j and k are the unit vectors along theWhat is the magnitude of the vector 3i − 4j + 12k?The vector from P(1, 2, 3) to Q(4, 6, 8) isThe vector from point P to point Q equals the position vector ofThe point dividing A(2, 0, 4) and B(8, 6, 10) in the ratio 1:2 internally has position vectorThe midpoint of the segment joining (2, 4, 6) and (4, 8, 10) has position vectorWhen R is the midpoint of PQ, the ratio m : n in the section formula satisfiesFor nonzero vectors a and b with angle θ between them, a · b equalsFor nonzero vectors a and b, a · b = 0 means the vectors areThe dot product of (2, 3, 1) and (1, −1, 4) isCompute (3i − j + 2k) · (i + 4j + 5k).The angle between the vectors i and i + j isThe vectors λi + 3j + k and 2i − j − 3k are perpendicular when λ equalsThe projection of 4i + 5j + 3k on 2i + 2j + k isThe projection of a on b is negative when the angle between them isFor any two vectors, |a + b| and |a| + |b| are related byIf |a| = 3 and |b| = 5, the greatest possible value of a · b isThe cross product a × b isWhich of these statements about the cross product is correct?For any vector a, the value of a × a isIf two nonzero vectors are parallel, their cross product isIf |a| = 4, |b| = 3 and the angle between them is 30°, then |a × b| isA triangle has two sides given by vectors a and b. Its area isA parallelogram has adjacent sides 2i + j and i + 3j. Its area isTwo sides of a triangle are the vectors 3i and 4j. Its area isFor a = i + j and b = j + k, the vector a × b isFor any plane, the number of unit vectors perpendicular to it isWhich relation holds for every pair of vectors a and b?The scalar triple product of three vectors gives the volume of aThe direction cosines of 2i − 3j + 6k areThe vectors 2i + 4j − 6k and i + 2j − 3k areIf xi + 3j − k equals 2i + yj + zk, then x + y + z isTwo perpendicular vectors have magnitudes 6 and 8. The magnitude of their sum isUnit vectors a and b satisfy |a + b| = 1. The angle between them isThe triangle with vertices (1, 0, 0), (0, 1, 0) and (0, 0, 1) has areaIf a · b equals |a||b| for nonzero vectors, the angle between them is