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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  be unit vectors suppose that   and that the angle between   is      (1981 - 2 Marks)

Ans. T

Solution.  are three unit vectors such that

and angle between

Now eq. (1) shows that   perpendicular to both

is any scalar..

(as π/6 is the angle between

∴ 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.

Oth er wise if   are coplanar

∴ 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   and   respectively..

Then,

Similarly,

Clearly

⇒ A,B, C are collinear

∴ Statement is true.

Q. 4. For any three vectors              (1989 - 1 Mark)

Ans. F

Solution. For any three vectors   we have

∴ The given statement is false.

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