If ` A(3/sqrt(2), sqrt(2))`, `B(-3/sqrt(2), sqrt(2)), C(-3/sqrt(2), -sqrt(2))` and `D(3 cos theta , 2 sin theta)` are four points . If the area of the

Question

If ` A(3/sqrt(2), sqrt(2))`, `B(-3/sqrt(2), sqrt(2)), C(-3/sqrt(2), -sqrt(2))` and `D(3 cos theta , 2 sin theta)` are four points . If the area of the

If ` A(3/sqrt(2), sqrt(2))`, `B(-3/sqrt(2), sqrt(2)), C(-3/sqrt(2), -sqrt(2))` and `D(3 cos theta , 2 sin theta)` are four points . If the area of the quadrilateral ABCD is maximum where `theta in (3 pi/2, 2 pi)` then (a) maximum area is 10 sq units (b) `theta = 7 pi/4` (c) `theta = 2 pi- sin^(-1) 3/ sqrt(85)` (d) maximum area is 12 sq units

Monjur Alahi

6 views

2025-01-04 04:42

1 Answers

Related Questions

Let `A=[{:(,sin theta,1sqrt2),(,-1//sqrt2,cos theta),(,cos theta,tan theta):}]& B=[{:(,1sqrt2,sin theta),(,cos theta,cos theta),(,cos theta,-1):}]`. F

2 Answers 4 Views

Prove the orthogonal matrices of order two are of the form `[(cos theta,-sin theta),(sin theta,cos theta)]` or `[(cos theta,sin theta),(sin theta,-cos

2 Answers 7 Views

Find the characteristic roots of the two-rowed orthogonal matrix `[(cos theta,-sin theta),(sin theta,cos theta)]` and verify that they are of unit mod

2 Answers 6 Views

If `theta-phi=pi/2,` prove that, `[(cos^2 theta,cos theta sin theta),(cos theta sin theta,sin^2 theta)] [(cos^2 phi,cos phi sin phi),(cos phi sin phi,

2 Answers 5 Views

If `A(theta)=[(sin theta, i cos theta),(i cos theta, sin theta)]`, then which of the following is not true ?

2 Answers 7 Views

Find the principal values of the following (i) `sin^(-1) (sin 1)` (ii) `sin^(-1) (sin 2)` (iii) `sin^(-1) (sin 10)` (iv) `sin^(-1) (sin 20)` (v) `sin^

2 Answers 5 Views

Find the principal value of the following (i) `cos^(-1) (cos 3)` (ii) `cos^(-1) (cos 4)` (iii) `cos^(-1) (cos 15)` (iv) `cos^(-1) (cos 30)` (v) `cos^(

2 Answers 4 Views

If equation `sin^(-1) (4 sin^(20 theta + sin theta) + cos^(-1) (6 sin theta - 1) = (pi)/(2)` has 10 solution for `theta in [0, n pi]`, then find the m

2 Answers 6 Views

The value of `sin^(-1)[xsqrt(1-x)-sqrt(x)sqrt(1-x^2)]` is equal to `sin^(-1)x+sin^(-1)sqrt(x)` `sin^(-1)x-sin^(-1)sqrt(x)` `sin^(-1)sqrt(x)-sin^(-1)x`

2 Answers 5 Views

सरल कीजिए, ` cos theta [{:( cos theta,, sin theta ), (-sin theta,, cos theta ):}] + sin theta [ {:(sin theta ,, - cos theta ), (cos theta ,, sin theta

2 Answers 4 Views

Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Area of qudrilateral AbCD is maximum when area of ACD is maximum. Area of triangle ACD.
`Delta_1=(1)/(2)||{:(3/sqrt2,,sqrt2,,),(3/sqrt2,,-sqrt2,,),(3sintheta,,2costheta,,),(3/sqrt2,,sqrt2,,):}||`
`=|-3sqrt(2)costheta+3sqrt(2)sintheta|`
`therefore Delta_1("max")=6`, when`theta=(7pi)/(4)` (as `theta epsilon(3pi//2,2pi`))
Maximum area is 12 sq.units (as ABCD is a rectangle).