Vector Algebra: JEE Main Mathematics Previous Year Questions

461 previous year questions from Vector Algebra. Here are the 25 most important ones; open any question for the correct answer and a full step-by-step solution.

1. $If the volume of the tetrahedron formed by the coterminous edgcs a, b and c is 4 , then the volume of the parallelopiped formed by the coterminous edges\dots$
2. $The set of all α, for which the vectors a = αt i + 6 j - 3 k and b = t i - 2 j - 2 αt k are inclined at an obtuse angle for all t \in R, is$
3. $Let a, b, c be three-unit vectors satisfying | a - b |^{2} + | a - c |^{2} = 10. Then Statement (I) :\dots$
4. $Let a = i + x j + k, b = i + j + k, and | a + b | = | a | + | b | then$
5. $If cos α, cos β, cos γ are the direction cosines of a vector a, then\dots$
6. $Let a = 2 i + j - 2 k and b = i + j . If c is a vector such that a \cdot c = | c |, | c - a | = 22 and the angle between a \times b and\dots$
7. $If the magnitudes of a, b and a + b are respectively 3,4 and 5 , then the magnitude of (a - b) is$
8. $If a = 2 i^+ j^+ 3 k^, b = i^+ 3 j^- k^and c = 3 i^- j^- 2 k^, then the value of\dots$
9. $If the area of the parallelogram with a and b as two adjacent sides is 15 sq. units, then the area of the parallelogram having 3 a + 2 b and a + 3 b as two adjacent\dots$
10. $Let a = 2 i + 3 j + k, b = 4 i + j, c = i - 3 j - 7 k If r = x i + y j + z k, r \cdot a = 9, r \cdot b = 7, r \cdot c = 6 then (x, y, z) =$
11. $If a and b are unit vectors and α is the angle between them, then a + b is a unit vector when cos α =$
12. $Let a unit vector which makes an angle of 60^{\circ} with 2 i + 2 j - k and angle 45^{\circ} with i - k be C . Then\dots$
13. $If a = (2 x + y) i + 3 j + 9 k and b = 2 i + j - (x - y) k are two collinear vectors, then x^{3} + 27 y^{3} =$
14. $Let a and b be two vectors such that | a | = 1, | b | = 4 and a \cdot b = 2 . If c = (2 a \times b) - 3 b and the angle betwee\dots$
15. $If (k, 1, 5), (1, 0, 3), (7, - 2, m) are collinearr then\dots$
16. $If a = (1, 2, 3), b = (2, - 1, 1), c = (3, 2, 1) and\dots$
17. $Let a = i + 2 j + k, b = 3 (i - j + k) . Let c be the vector such that a \times c = b and a \cdot c = 3 . Then\dots$
18. $The triad (x, y, z) of real number such that (3 i - j + 2 k) = (2 i + 3 j - k) x + \dots$
19. $If ABCD is a cyclic quadrilateral with R as the radius of the circumcircle and (AB)^{2} + (CD)^{2} = 4 R^{2} th\dots$
20. $Let P be a point in the plane of the vectors AB = 3 i + j - k and AC = i - j + 3 k such that P is equidistant from the lines AB and AC . If\dots$
21. $Let a = 2 i - 3 j + 4 k, b = 7 i + 2 j - 3 k, c = i + j + k . The vector x such that x, c = 60 and perpendicular to both a, b is$
22. $If α is the angle between two vector p = 3 i + 4 j - k and q = 2 i - j + k, then sin (α) =$
23. $Let three vectors a, b and c be such that c is coplanar with a and b, a \cdot c = 7 and b is perpendicular to c where a = - i + j + k and b = 2 i + k \dots$
24. $If P, Q are two points on the curve y = 2^{x + 2} in the rectangular Cartesian coordinate system such that OP \cdot i = - 1, OQ \cdot i = 2 then\dots$
25. $If the lines x = ay + b, z = cy + d and x = a'z + b', y = c'z + d' are perpendicular, then :$

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Vector Algebra: JEE Main Mathematics Previous Year Questions

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