Vector Algebra PYQs Set 16 (PDF)

Set 16 of 16 · Questions 451-461 of 461

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Mere Teacher · Previous Year Questions JEE Main Mathematics · Vector Algebra · Set 16 (Q451-461)
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451. $The distance of the point having position vector - i + 2 j + 6 k from the straight line passing through the point (2, 3 , -4) and parallel to the vector , 6 i + 3 j - 4 k is :$ (1) $7$ (2) $43$ (3) $6$ 452. $If i + j - k and 2 i - 3 j + k are adjacent sides of a parallelogram, then the lengths of its diagonals are$ (1) $21, 13$ (2) $3, 14$ (3) $13, 14$ (4) $21, 3$ 453. $Let a = 5 i - j - 3 k and b = i + 3 j - 5 k be two vectors. Then which one of the following statements is TRUE?$ (1) $Projection of a on b is \frac{17}{35} and the direction of the projection vector is same as of b?$ (2) $Projection of a on b is \frac{27}{35} and the direction of the projection vector is opposite to the direction of b$ (3) $Projection of a on b is \frac{- 17}{35} and the direction of the projection vector is same as of b$ (4) $Projection of a on b is \frac{- 17}{35} and the direction of the projection vector is opposite to the direction of b$ 454. $If the volume of the parallelepiped formed by three non-coplanar vector a, b and c is 4 cubic units, then (a \times bb \times cc \times a) =$ (1) $8$ (2) $64$ (3) $16$ (4) $4$ 455. $If then λ is equal to$ (1) $0$ (2) $1$ (3) $2$ (4) $3$ 456. $Let a = i^+ 4 j^+ 2 k^, b = 3 i^- 2 j^+ 7 k^and c = 2 i^- j^+ 4 k^. If a vector d satisfies d \times b = c \times b and d \cdot a = 24, then ∣ d ∣^{2} is equal to$ (1) $323$ (2) $423$ (3) $313$ (4) $413$ 457. $If \| a \| = 5, \| b \| = 3, \| c \| = 4 and a is perpendicular to b and c such that angle between b and c is \frac{5 π}{6}, then [ab c] =$ (1) $20$ (2) $30$ (3) $12$ (4) $25$ 458. $Let the volume of the tetrahedron with vertices i - j - 2 k, - 2 i + j - 2 k, - i - 2 j + k, 2 i + 2 j + ak be \frac{20}{3} Then the integral value of a is$ (1) $-2$ (2) $1$ (3) $-1$ (4) $2$ 459. $Let a = α i^+ 3 j^- k^, b = 3 i^- β j^+ 4 k^and c = i^+ 2 j^- 2 k^where α, β \in R, be three vectors. If the projection of a on c is \frac{10}{3} and b \times c = - 6 i^+ 10 j^+ 7 k^,then the value of α + β equal to$ (1) $3$ (2) $4$ (3) $5$ (4) $6$ 460. $If a . b = 1, b . c = 2 and c . a = 3, then the value of is:$ (1) $0$ (2) $- 6 a \cdot (b \times c)$ (3) $12 c \cdot (a \times b)$ (4) $- 12 b \cdot (c \times a)$ 461. $Let λ be an integer. If the shortest distance between the lines x - λ = 2 y - 1 = - 2 z and x = y + 2 λ = z - λ is \frac{7}{2 2}, then the value of ∣ λ ∣ is$