CA Foundation Exam > CA Foundation Questions > Let P = (1, 2, x), Q = (a, x, y), R = (x, y, ...
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Let P = (1, 2, x), Q = (a, x, y), R = (x, y, z) the set (R×Q)∩(R×P) is
- a){(a, x) (a, y) (a, z); (x, x) (x, y) (x, z); (y, x) (y, y) (y, z)}
- b){(1, x) (1, y) (2, x) (2, y) (x, x) (x, y)}
- c){(x, x) (y, x) (z, x)}
- d){(1, a) (1, x) (1, y) (2, a) (2, x) (2, y) (x, a) (x, x) (x, y) (x, 1) (x, 2) (y, 1) (y, 2) (y, x) (z, 1) (z, 2) (z, x)}
Correct answer is option 'C'. Can you explain this answer?
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Let P = (1, 2, x), Q = (a, x, y), R = (x, y, z) the set (R×Q)&ca...
The set of points that lie on the plane containing P, Q, and R can be found by first finding two vectors that lie in the plane and then taking their cross product. One possible approach is to use the vectors PQ and PR:
PQ = (a-1, x-2, y-x)
PR = (x-1, y-2, z-2)
Taking the cross product of PQ and PR gives a normal vector to the plane:
PQ x PR = (y-x)(z-2) - (y-2)(x-2), (a-1)(z-2) - (y-2)(x-1), (a-1)(y-x) - (z-2)(a-1)
We want the equation of the plane in the form ax + by + cz = d. To do this, we can use the point-normal form of the equation of a plane:
a(x-x0) + b(y-y0) + c(z-z0) = 0
where (x0, y0, z0) is any point on the plane and (a, b, c) is the normal vector to the plane. Plugging in P = (1, 2, x) gives:
a(x-1) + b(y-2) + c(z-x) = 0
We can solve for d by plugging in R = (x, y, z):
a(x-1) + b(y-2) + c(z-x) = d
a(x-1) + b(y-2) + c(z-x) = a(x-1) + b(y-2) + c(z-x)
a(x-1) + b(y-2) + c(z-x) = ax + by + cz - a - 2b
d = ax + by + cz - a - 2b
Substituting in the components of P, Q, and R, we get:
d = ax + (y-2)(z-x) - a - 2(x-2), which simplifies to:
d = ax + yz - 2y - 2x + 4 - a
So the equation of the plane containing P, Q, and R is:
ax + yz - 2y - 2x + 4 - a = d
or
ax + yz - 2y - 2x + 4 - a = ax + by + cz
PQ = (a-1, x-2, y-x)
PR = (x-1, y-2, z-2)
Taking the cross product of PQ and PR gives a normal vector to the plane:
PQ x PR = (y-x)(z-2) - (y-2)(x-2), (a-1)(z-2) - (y-2)(x-1), (a-1)(y-x) - (z-2)(a-1)
We want the equation of the plane in the form ax + by + cz = d. To do this, we can use the point-normal form of the equation of a plane:
a(x-x0) + b(y-y0) + c(z-z0) = 0
where (x0, y0, z0) is any point on the plane and (a, b, c) is the normal vector to the plane. Plugging in P = (1, 2, x) gives:
a(x-1) + b(y-2) + c(z-x) = 0
We can solve for d by plugging in R = (x, y, z):
a(x-1) + b(y-2) + c(z-x) = d
a(x-1) + b(y-2) + c(z-x) = a(x-1) + b(y-2) + c(z-x)
a(x-1) + b(y-2) + c(z-x) = ax + by + cz - a - 2b
d = ax + by + cz - a - 2b
Substituting in the components of P, Q, and R, we get:
d = ax + (y-2)(z-x) - a - 2(x-2), which simplifies to:
d = ax + yz - 2y - 2x + 4 - a
So the equation of the plane containing P, Q, and R is:
ax + yz - 2y - 2x + 4 - a = d
or
ax + yz - 2y - 2x + 4 - a = ax + by + cz
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Let P = (1, 2, x), Q = (a, x, y), R = (x, y, z) the set (R×Q)∩(R×P) isa){(a, x) (a, y) (a, z); (x, x) (x, y) (x, z); (y, x) (y, y) (y, z)}b){(1, x) (1, y) (2, x) (2, y) (x, x) (x, y)}c){(x, x) (y, x) (z, x)}d){(1, a) (1, x) (1, y) (2, a) (2, x) (2, y) (x, a) (x, x) (x, y) (x, 1) (x, 2) (y, 1) (y, 2) (y, x) (z, 1) (z, 2) (z, x)}Correct answer is option 'C'. Can you explain this answer?
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Let P = (1, 2, x), Q = (a, x, y), R = (x, y, z) the set (R×Q)∩(R×P) isa){(a, x) (a, y) (a, z); (x, x) (x, y) (x, z); (y, x) (y, y) (y, z)}b){(1, x) (1, y) (2, x) (2, y) (x, x) (x, y)}c){(x, x) (y, x) (z, x)}d){(1, a) (1, x) (1, y) (2, a) (2, x) (2, y) (x, a) (x, x) (x, y) (x, 1) (x, 2) (y, 1) (y, 2) (y, x) (z, 1) (z, 2) (z, x)}Correct answer is option 'C'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Let P = (1, 2, x), Q = (a, x, y), R = (x, y, z) the set (R×Q)∩(R×P) isa){(a, x) (a, y) (a, z); (x, x) (x, y) (x, z); (y, x) (y, y) (y, z)}b){(1, x) (1, y) (2, x) (2, y) (x, x) (x, y)}c){(x, x) (y, x) (z, x)}d){(1, a) (1, x) (1, y) (2, a) (2, x) (2, y) (x, a) (x, x) (x, y) (x, 1) (x, 2) (y, 1) (y, 2) (y, x) (z, 1) (z, 2) (z, x)}Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let P = (1, 2, x), Q = (a, x, y), R = (x, y, z) the set (R×Q)∩(R×P) isa){(a, x) (a, y) (a, z); (x, x) (x, y) (x, z); (y, x) (y, y) (y, z)}b){(1, x) (1, y) (2, x) (2, y) (x, x) (x, y)}c){(x, x) (y, x) (z, x)}d){(1, a) (1, x) (1, y) (2, a) (2, x) (2, y) (x, a) (x, x) (x, y) (x, 1) (x, 2) (y, 1) (y, 2) (y, x) (z, 1) (z, 2) (z, x)}Correct answer is option 'C'. Can you explain this answer?.
Let P = (1, 2, x), Q = (a, x, y), R = (x, y, z) the set (R×Q)∩(R×P) isa){(a, x) (a, y) (a, z); (x, x) (x, y) (x, z); (y, x) (y, y) (y, z)}b){(1, x) (1, y) (2, x) (2, y) (x, x) (x, y)}c){(x, x) (y, x) (z, x)}d){(1, a) (1, x) (1, y) (2, a) (2, x) (2, y) (x, a) (x, x) (x, y) (x, 1) (x, 2) (y, 1) (y, 2) (y, x) (z, 1) (z, 2) (z, x)}Correct answer is option 'C'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Let P = (1, 2, x), Q = (a, x, y), R = (x, y, z) the set (R×Q)∩(R×P) isa){(a, x) (a, y) (a, z); (x, x) (x, y) (x, z); (y, x) (y, y) (y, z)}b){(1, x) (1, y) (2, x) (2, y) (x, x) (x, y)}c){(x, x) (y, x) (z, x)}d){(1, a) (1, x) (1, y) (2, a) (2, x) (2, y) (x, a) (x, x) (x, y) (x, 1) (x, 2) (y, 1) (y, 2) (y, x) (z, 1) (z, 2) (z, x)}Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let P = (1, 2, x), Q = (a, x, y), R = (x, y, z) the set (R×Q)∩(R×P) isa){(a, x) (a, y) (a, z); (x, x) (x, y) (x, z); (y, x) (y, y) (y, z)}b){(1, x) (1, y) (2, x) (2, y) (x, x) (x, y)}c){(x, x) (y, x) (z, x)}d){(1, a) (1, x) (1, y) (2, a) (2, x) (2, y) (x, a) (x, x) (x, y) (x, 1) (x, 2) (y, 1) (y, 2) (y, x) (z, 1) (z, 2) (z, x)}Correct answer is option 'C'. Can you explain this answer?.
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Here you can find the meaning of Let P = (1, 2, x), Q = (a, x, y), R = (x, y, z) the set (R×Q)∩(R×P) isa){(a, x) (a, y) (a, z); (x, x) (x, y) (x, z); (y, x) (y, y) (y, z)}b){(1, x) (1, y) (2, x) (2, y) (x, x) (x, y)}c){(x, x) (y, x) (z, x)}d){(1, a) (1, x) (1, y) (2, a) (2, x) (2, y) (x, a) (x, x) (x, y) (x, 1) (x, 2) (y, 1) (y, 2) (y, x) (z, 1) (z, 2) (z, x)}Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Let P = (1, 2, x), Q = (a, x, y), R = (x, y, z) the set (R×Q)∩(R×P) isa){(a, x) (a, y) (a, z); (x, x) (x, y) (x, z); (y, x) (y, y) (y, z)}b){(1, x) (1, y) (2, x) (2, y) (x, x) (x, y)}c){(x, x) (y, x) (z, x)}d){(1, a) (1, x) (1, y) (2, a) (2, x) (2, y) (x, a) (x, x) (x, y) (x, 1) (x, 2) (y, 1) (y, 2) (y, x) (z, 1) (z, 2) (z, x)}Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Let P = (1, 2, x), Q = (a, x, y), R = (x, y, z) the set (R×Q)∩(R×P) isa){(a, x) (a, y) (a, z); (x, x) (x, y) (x, z); (y, x) (y, y) (y, z)}b){(1, x) (1, y) (2, x) (2, y) (x, x) (x, y)}c){(x, x) (y, x) (z, x)}d){(1, a) (1, x) (1, y) (2, a) (2, x) (2, y) (x, a) (x, x) (x, y) (x, 1) (x, 2) (y, 1) (y, 2) (y, x) (z, 1) (z, 2) (z, x)}Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Let P = (1, 2, x), Q = (a, x, y), R = (x, y, z) the set (R×Q)∩(R×P) isa){(a, x) (a, y) (a, z); (x, x) (x, y) (x, z); (y, x) (y, y) (y, z)}b){(1, x) (1, y) (2, x) (2, y) (x, x) (x, y)}c){(x, x) (y, x) (z, x)}d){(1, a) (1, x) (1, y) (2, a) (2, x) (2, y) (x, a) (x, x) (x, y) (x, 1) (x, 2) (y, 1) (y, 2) (y, x) (z, 1) (z, 2) (z, x)}Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Let P = (1, 2, x), Q = (a, x, y), R = (x, y, z) the set (R×Q)∩(R×P) isa){(a, x) (a, y) (a, z); (x, x) (x, y) (x, z); (y, x) (y, y) (y, z)}b){(1, x) (1, y) (2, x) (2, y) (x, x) (x, y)}c){(x, x) (y, x) (z, x)}d){(1, a) (1, x) (1, y) (2, a) (2, x) (2, y) (x, a) (x, x) (x, y) (x, 1) (x, 2) (y, 1) (y, 2) (y, x) (z, 1) (z, 2) (z, x)}Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice CA Foundation tests.
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