Vector Algebra

JEE Main 2025 (Online) 23rd January Morning ShiftMCQHard📈 Topic in 55% papers+4−1

Ques. 1JEE Main 2025, 23 January (Morning Shift)

Let the position vectors of the vertices A, B and C of a tetrahedron ABCD be i+2 j+ k, i+3 j-2 k and 2 i+ j- k respectively. The altitude from the vertex D to the opposite face ABC meets the median line segment through A of the triangle ABC at the point E. If the length of AD is 1103 and the volume of the tetrahedron is 8056 2, then the position vector of E is

16 (7 i+12 j+ k )
112 (7 i+4 j+3 k )
16 (12 i+12 j+ k )
12 ( i+4 j+7 k )

Answer

(1) 16 (7 i+12 j+ k )

Solution

AB AC=-5 i-3 j- k area of ABC= 352

[figure]

Volume = 13(area) DE DE= 232, and DE plane, so in right ADE: AE2= 1109- 232= 1318

Mid-point of BC: M ( 32,2,- 32 ), AM= 12(1,0,-5), and E lies on AM

AE= 1318 (1,0,-5) 26= 16(1,0,-5)

E= 16 (7 i+12 j+ k )

Answer: (1)

Keep practising — Vector Algebra

Ques. 2JEE Main 2025, 23 January (Morning Shift)

Let the arc AC of a circle subtend a right angle at the centre O. If the point B on the arc AC, divides the arc AC such that length of arc ABlength of arc BC= 15, and OC= OA+ OB, then + 2( 3-1) is equal to

2 3
5 3
2+ 3
2- 3

Ques. 3JEE Main 2025, 23 January (Evening Shift)

Let the point A divide the line segment joining the points P(-1,-1,2) and Q(5,5,10) internally in the ratio r:1 (r>0). If O is the origin and ( OQ OA )- 15 | OP OA |2=10, then the value of r is :

Ques. 4JEE Main 2025, 22 January (Morning Shift)

Let c be the projection vector of b= i+4 k, >0, on the vector a= i+2 j+2 k. If | a+ c|=7, then the area of the parallelogram formed by the vectors b and c is .

Ques. 5JEE Main 2025, 22 January (Evening Shift)

Let a and b be two unit vectors such that the angle between them is 3. If a+2 b and 3 a- b are perpendicular to each other, then the number of values of in [-1,3] is :

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