Advertisements
Advertisements
प्रश्न
Choose the correct alternative:
If `|(2"a", x_1, y_1),(2"b", x_2, y_2),(2"c", x_3, y_3)| = "abc"/2 ≠ 0`, then the area of the triangle whose vertices are `(x_1/"a", y_1/"a"), (x_2/"b", y_2/"b"), (x_3/"c", y_3/"c")` is
विकल्प
`1/4`
`1/4 "abc"`
`1/8`
`1/8 "abc"`
Advertisements
उत्तर
`1/8`
APPEARS IN
संबंधित प्रश्न
Without expanding the determinant, prove that `|("s", "a"^2, "b"^2 + "c"^2),("s", "b"^2, "c"^2 + "a"^2),("s", "c"^2, "a"^2 + "b"^2)|` = 0
If `|("a", "b", "a"alpha + "b"),("b", "c", "b"alpha + "c"),("a"alpha + "b", "b"alpha + "c", 0)|` = 0, prove that a, b, c are in G. P or α is a root of ax2 + 2bx + c = 0
Show that `|("a"^2 + x^2, "ab", "ac"),("ab", "b"^2 + x^2, "bc"),("ac", "bc", "c"^2 + x^2)|` is divisiible by x4
If a, b, c, are all positive, and are pth, qth and rth terms of a G.P., show that `|(log"a", "p", 1),(log"b", "q", 1),(log"c", "r", 1)|` = 0
Without expanding, evaluate the following determinants:
`|(2, 3, 4),(5, 6, 8),(6x, 9x, 12x)|`
Using cofactors of elements of second row, evaluate |A|, where A = `[(5, 3, 8),(2, 0, 1),(1, 2, 3)]`
Show that `|(1, 1, 1),(x, y, z),(x^2, y^2, z^2)|` = (x – y)(y – z)(z – x)
Identify the singular and non-singular matrices:
`[(1, 2, 3),(4, 5, 6),(7, 8, 9)]`
Identify the singular and non-singular matrices:
`[(2, -3, 5),(6, 0, 4),(1, 5, -7)]`
Identify the singular and non-singular matrices:
`[(0, "a" - "b", "k"),("b" - "a", 0, 5),(-"k", -5, 0)]`
Determine the values of a and b so that the following matrices are singular:
A = `[(7, 3),(-2, "a")]`
Determine the values of a and b so that the following matrices are singular:
B = `[("b" - 1, 2, 3),(3, 1, 2),(1, -2, 4)]`
Choose the correct alternative:
If x1, x2, x3 as well as y1, y2, y3 are in geometric progression with the same common ratio, then the points (x1, y1), (x2, y2), (x3, y3) are
If Δ is the area and 2s the sum of three sides of a triangle, then
What is the value of Δ if, Δ = `|(0, sin alpha, - cos alpha),(-sin alpha, 0, sin beta),(cos alpha, - sin beta, 0)|`
Find the area of the triangle with vertices at the point given is (1, 0), (6, 0), (4, 3).
If `|(1 + x, x, x^2),(x, 1 + x, x^2),(x^2, x, 1 + x)|` = ax5 + bx4 + cx3 + dx2 + λx + µ be an identity in x, where a, b, c, d, λ, µ are independent of x. Then the value of λ is ______.
Let S = `{((a_11, a_12),(a_21, a_22)): a_(ij) ∈ {0, 1, 2}, a_11 = a_22}`
Then the number of non-singular matrices in the set S is ______.
If a, b, c, are non zero complex numbers satisfying a2 + b2 + c2 = 0 and `|(b^2 + c^2, ab, ac),(ab, c^2 + a^2, bc),(ac, bc, a^2 + b^2)|` = ka2b2c2, then k is equal to ______.
