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Find the coordinates of the foot of perpendicular and perpendicular distance from the point P(4,3,2) to the plane x + 2y + 3z = 2. Also find the image of P in the plane.
Concept: undefined >> undefined
Using properties of determinants, find the value of x for which
`|(4-"x",4+"x",4+"x"),(4+"x",4-"x",4+"x"),(4+"x",4+"x",4-"x")|= 0`
Concept: undefined >> undefined
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The product of any matrix by the scalar ______ is the null matrix.
Concept: undefined >> undefined
The value of `|(1, 1, 1),(""^"n""C"_1, ""^("n" + 2)"C"_1, ""^("n" + 4)"C"_1),(""^"n""C"_2, ""^("n" + 2)"C"_2, ""^("n" + 4)"C"_2)|` is 8.
Concept: undefined >> undefined
Evaluate: `|(x^2 - x + 1, x - 1),(x + 1, x + 1)|`
Concept: undefined >> undefined
Evaluate: `|("a" + x, y, z),(x, "a" + y, z),(x, y, "a" + z)|`
Concept: undefined >> undefined
Evaluate: `|(0, xy^2, xz^2),(x^2y, 0, yz^2),(x^2z, zy^2, 0)|`
Concept: undefined >> undefined
Evaluate: `|(3x, -x + y, -x + z),(x - y, 3y, z - y),(x - z, y - z, 3z)|`
Concept: undefined >> undefined
Evaluate: `|(x + 4, x, x),(x, x + 4, x),(x, x, x + 4)|`
Concept: undefined >> undefined
Evaluate: `|("a" - "b" - "c", 2"a", 2"a"),(2"b", "b" - "c" - "a", 2"b"),(2"c", 2"c", "c" - "a" - "b")|`
Concept: undefined >> undefined
Prove that: `|(y^2z^2, yz, y + z),(z^2x^2, zx, z + x),(x^2y^2, xy, x + y)|` = 0
Concept: undefined >> undefined
Prove that: `|(y + z, z, y),(z, z + x, x),(y, x, x + y)|` = 4xyz
Concept: undefined >> undefined
Prove that: `|("a"^2 + 2"a", 2"a" + 1, 1),(2"a" + 1, "a" + 2, 1),(3, 3, 1)| = ("a" - 1)^3`
Concept: undefined >> undefined
If A + B + C = 0, then prove that `|(1, cos"c", cos"B"),(cos"C", 1, cos"A"),(cos"B", cos"A", 1)|` = 0
Concept: undefined >> undefined
Find the value of θ satisfying `[(1, 1, sin3theta),(-4, 3, cos2theta),(7, -7, -2)]` = 0
Concept: undefined >> undefined
If `[(4 - x, 4 + x, 4 + x),(4 + x, 4 - x, 4 + x),(4 + x, 4 + x, 4 - x)]` = 0, then find values of x.
Concept: undefined >> undefined
The value of determinant `|("a" - "b", "b" + "c", "a"),("b" - "a", "c" + "a", "b"),("c" - "a", "a" + "b", "c")|` is ______.
Concept: undefined >> undefined
The determinant `|("b"^2 - "ab", "b" - "c", "bc" - "ac"),("ab" - "a"^2, "a" - "b", "b"^2 - "ab"),("bc" - "ac", "c" - "a", "ab" - "a"^2)|` equals ______.
Concept: undefined >> undefined
The number of distinct real roots of `|(sinx, cosx, cosx),(cosx, sinx, cosx),(cosx, cosx, sinx)|` = 0 in the interval `pi/4 x ≤ pi/4` is ______.
Concept: undefined >> undefined
If A, B and C are angles of a triangle, then the determinant `|(-1, cos"C", cos"B"),(cos"C", -1, cos"A"),(cos"B", cos"A", -1)|` is equal to ______.
Concept: undefined >> undefined
