TS EAPCET (Engineering) Vector Algebra — practice questions
77 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice TS EAPCET (Engineering) Vector Algebra in the app →The dot product (scalar product) of two vectors $\vec{a}$ and $\vec{b}$ is:Two non-zero vectors $\vec{a}$ and $\vec{b}$ are perpendicular if and only if:The cross product $\vec{a} \times \vec{b}$ of two vectors has magnitude:Two vectors of magnitudes $3$ and $4$ are perpendicular to each other. The magnitude of their resultant is:A quantity having only magnitude (no direction) is called:Vector addition is:The dot product ā · b̄ is:The cross product ā × b̄ is:What is î × ĵ?Two vectors are PERPENDICULAR iff:Two vectors are PARALLEL (or anti-parallel) iff:The MAGNITUDE of a × b equals:Find magnitude of ā = 3î + 4ĵ:Find ā · b̄ if ā = 2î + 3ĵ and b̄ = î - 2ĵ:Find ā × b̄ where ā = î + 2ĵ + k̂ and b̄ = 2î + ĵ + 3k̂:Angle between two vectors ā = 2î + 2ĵ and b̄ = 4î - 4ĵ:Find unit vector in direction of ā = 3î + 4ĵ:Area of parallelogram formed by ā and b̄ equals:Position vectors of P and Q are p̄ and q̄. The point R divides PQ internally in ratio m:n. Position vector of Three vectors ā, b̄, c̄ are coplanar iff their SCALAR TRIPLE PRODUCT [ā b̄ c̄] equals:For vectors ā = î + ĵ and b̄ = î - ĵ, find |ā + b̄|:Projection of ā = 3î + 4ĵ on b̄ = î + ĵ:If ā × b̄ = 0 and neither is the zero vector, then:Volume of parallelepiped formed by ā, b̄, c̄:For unit vectors î, ĵ, k̂: î · ĵ + ĵ · k̂ + k̂ · î =For vectors ā = î - ĵ + 2k̂ and b̄ = 3î + 2ĵ - k̂, find the AREA of the parallelogram formed (use |ā × b̄|):Find cos θ for ā = 2î + 3ĵ - 4k̂ and b̄ = î + 2ĵ + 3k̂ (where θ is the angle between them):Find scalar triple product [î ĵ k̂]:Vectors ā = î + 2ĵ + 3k̂ and b̄ = 2î + 3ĵ + αk̂ are perpendicular. Find α:For vectors ā = î - ĵ + 2k̂ and b̄ = 3î + 2ĵ - k̂, find the area of triangle formed:Find angle θ between ā = 2î + 3ĵ - 4k̂ and b̄ = î + 2ĵ + 3k̂ (use cos θ = ā·b̄/(|ā||b̄|)):For ā = 2î + 3ĵ and b̄ = αî + 6ĵ to be parallel, α equals:If [ā b̄ c̄] = 5, find [2ā b̄ c̄]:Vector r̄ is collinear with ā = î - 2ĵ + 2k̂ and |r̄| = 12. Find r̄: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 equalsTwo 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 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 byWhich 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