CUET Level II JEE Mock Test-3 (Mathematics 2024-2025)

Let a = a₁i + a₂j + a₃k a_i > 0, i =1,2,3 be a vector which makes equal angles with the coordinates axes OX, OY and OZ. Also, let the projection of a on the vector 3i + 4j be 7. Let b a vector obtained by rotating a with 90⁰. If a, b and x-axis are coplanar, then projection of a vector b on 3i + 4j is equal to

• √7

• √2

• 2

• 7

If l a + b l = l a - b l then the vectors a and b are adjacent sides of

• a rectangle

• a square

• a rhombus

• none of these

ABC is a triangle and P is any point on BC such that PQ is the resultant of the vectors AP, PB and PC, then

• the position of Q depends on position of P

• Q is a fixed point

• Q lies on AB or AC

• None of these

ABCDEF is a regular hexagon where centre O is the origin. If the position vectors of A and B are i -j +2k and 2i +j -k respectively, then BC is equal to

• i + j - 2k

• • - i + j -2k

• 3i + 3j -4k

• None of these

If a = i + 2j + 3k, b = 2i + 3j + k, c = 3i + j + 2k and αa + βb + γc = -3(i - k), then the ordered triplet ( α, β, γ ) is

• (2, -1, -1)

• (-2, 1, 1)

• (-2, -1, 1)

• (2, 1, -1)

Consider points A, B, C and D with position vectors 7i -4j + 7k, i -6j + 10k, -i -3j + 4k and 5i - j + 5k respectively. then ABCD is a

• parallelogram but not a rhombus

• square

• rhombus

• none of these

If the position vectors of the vertices A, B, C of a triangle ABC are 7j + 10k, -i + 6j + 6k and -4i + 9j + 6k respectively, the triangle is :

• equilateral

• isosceles

• scalene

• right angled and isosceles also

In triangle ABC, which of the following is not true?

• AB + BC + CA = 0

• AB + BC - AC = 0

• AB + BC - CA + 0

• AB - CB + CA = 0

If two vertices of a triangle are i - j and j + k, then the third vertex can be

• i + k

• i - 2j - k and -2i - j

• i - k

• all the above

The figure formed by the four points i + j - k, 2i + 3j, 5j - 2k and k - j is

• trapezium

• rectangle

• parallelogram

• none of these