∣ ∣ ∣ ∣ 1 a b − a 1 c − b − c 1 ∣ ∣ ∣ ∣ = Options: A . &nbsp1+a2+b2+c2 B . &nbsp1−a2+b2+c2 C . &nbsp1+a2+b2−c2 D . &nbsp1+a2−b2+c2

Answer: Option A : A ∣ ∣ ∣ ∣ 1 a b − a 1 c − b − c 1 ∣ ∣ ∣ ∣ = 1 ( 1 + c 2 ) − a ( − a + b c ) + b ( a c + b ) = 1 + a 2 + b 2 + c 2 .

∣∣ ∣∣1ab−a1c−b−c1∣Ȣ

Question

∣ ∣∣ ∣ \begin{matrix} 1 & a & b - a & 1 & c - b & - c & 1 \end{matrix} ∣ ∣∣ ∣ =

Options:

A . 1+a2+b2+c2

B . 1−a2+b2+c2

C . 1+a2+b2−c2

D . 1+a2−b2+c2

Answer: Option A
:
A

∣ ∣∣ ∣ \begin{matrix} 1 & a & b - a & 1 & c - b & - c & 1 \end{matrix} ∣ ∣∣ ∣ = 1 (1 + c^{2}) - a (- a + b c) + b (a c + b) = 1 + a^{2} + b^{2} + c^{2}

Was this answer helpful ?

Next Question

Question 1. If a,b,c are non – zero real numbers and if the equations (a-1) x = y + z, (b -1)y = z + x, (c - 1)z = x + ....solution, then ab + bc + ca is equal to

Question 2. If Dk=∣∣ ∣ ∣∣1nn2kn2+n+1n2+n2k−1n2n2+n+1∣∣ ∣ ∣....If Dk=∣∣ ∣ ∣∣1nn2kn2+n+1n2+n2k−1n2n2+n+1∣∣ ∣ ∣∣ and ∑nk=1Dk=56, then n equals

Question 3. If A+B+C=π, then ∣∣ ∣ ∣∣sin(A+B+C)sinBcosC−sinB0tanAcos(A+B)−tnaA....If A+B+C=π, then ∣∣ ∣ ∣∣sin(A+B+C)sinBcosC−sinB0tanAcos(A+B)−tnaA0∣∣ ∣ ∣∣ is equal to

Question 4. If ω is a cube root of unity and Δ = ∣∣∣12ωωω2∣"....root of unity and Δ = ∣∣∣12ωωω2∣∣∣, then Δ2 is equal to

Question 5. The system of equations x + y + z =2, 3x − y + 2z =6 and 3....The system of equations x + y + z =2, 3x − y + 2z =6 and 3x + y + z =−18 has

Question 6. ....

Question 7. If Δ1 = ∣∣∣10ab∣∣∣ and Δ2 = ∣∣&#....If Δ1 = ∣∣∣10ab∣∣∣ and Δ2 = ∣∣∣10cd∣∣∣, then Δ2Δ1 is equal to

Question 8. The system of equationsX+2y+3z=42x+3y+4z=53x+4y+5z=6 has....

Question 9. ....

Question 10. If f, g and h are differentiable functions of x and △#....If f, g and h are differentiable functions of x and △⎛⎜ ⎜⎝x⎞⎟ ⎟⎠=∣∣ ∣ ∣∣fgh(xf)'(xg)'(xh)'(x2f)''(x2g)''(x2h)''∣∣ ∣ ∣∣,then △'⎛⎜ ⎜⎝x⎞⎟ ⎟⎠ is

Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)

Direction Sense Test Part 1 Reasoning (Hindi)

Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE

Cube & Cuboid Part 1 Reasoning (Hindi)

Data Interpretation (DI) Basic Concept Reasoning (Hindi)

Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)

Sail E0 free webinar Webinars

Real Numbers Part 7 Class 10 Maths

Real Numbers Part 1 Class 10 Maths

Polynomials Part 1 Class 10 Maths

DSP Combined 1 Free Revision Test SAIL JO E-0

GPOE / GPA Combined 1 Free Revision Test SAIL JO E-0

BSP Plant Specific Review Test SAIL JO E-0

BSL Combined 1 Free Revision Test SAIL JO E-0

GFM Combined 1 Free Revision Test SAIL JO E-0