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True/False: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

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True / False

Q. 1. Let True/False: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE be unit vectors suppose that  True/False: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE and that the angle between  True/False: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE is True/False: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE     (1981 - 2 Marks)

Ans. T

Solution. True/False: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE are three unit vectors such that 

True/False: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

and angle between  True/False: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Now eq. (1) shows that  True/False: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE perpendicular to both  True/False: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

True/False: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE  is any scalar.. 

True/False: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

(as π/6 is the angle between  True/False: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

True/False: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

∴ Given statement is true.


Q. 2. If  X. A = 0, X.B = 0, X.C = 0 for some non-zero vector X, then [A B C] = 0           (1983 - 1 Mark)

Ans. T

Solution. 

True/False: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
True/False: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Oth er wise if  True/False: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE are coplanar True/False: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

∴ Given statement is true. 


Q. 3. The points with position vectors  a + b, a – b, and a + kb are collinear for all real values of k.        (1984 - 1 Mark)

Ans. T

Solution. Let position vectors of pts A, B and C be  True/False: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE and  True/False: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE respectively.. 

Then,  True/False: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Similarly,  True/False: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Clearly  True/False: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

⇒ A,B, C are collinear  True/False: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

∴ Statement is true.

Q. 4. For any three vectors  True/False: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEETrue/False: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE            (1989 - 1 Mark)

Ans. F

Solution. For any three vectors  True/False: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE we have

True/False: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
True/False: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEETrue/False: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
True/False: Vector Algebra and Three Dimensional Geometry | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

∴ The given statement is false.

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