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Vector Algebra: Scalar Triple Product(23 Nov) - JEE MCQ


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10 Questions MCQ Test - Vector Algebra: Scalar Triple Product(23 Nov)

Vector Algebra: Scalar Triple Product(23 Nov) for JEE 2024 is part of JEE preparation. The Vector Algebra: Scalar Triple Product(23 Nov) questions and answers have been prepared according to the JEE exam syllabus.The Vector Algebra: Scalar Triple Product(23 Nov) MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Vector Algebra: Scalar Triple Product(23 Nov) below.
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Vector Algebra: Scalar Triple Product(23 Nov) - Question 1

For unit vectors b and c and any non zero vector a, the value of {{(a + b) × (a + c)}×(b × c)}⋅(b + c) is

Detailed Solution for Vector Algebra: Scalar Triple Product(23 Nov) - Question 1

The given expression

Vector Algebra: Scalar Triple Product(23 Nov) - Question 2

The vector ((i−j) × (j−k)) × (i + 5k) is equal to

Detailed Solution for Vector Algebra: Scalar Triple Product(23 Nov) - Question 2

The given expression

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Vector Algebra: Scalar Triple Product(23 Nov) - Question 3

If , and  are linearly dependent vectors and , then

Detailed Solution for Vector Algebra: Scalar Triple Product(23 Nov) - Question 3

Vector Algebra: Scalar Triple Product(23 Nov) - Question 4

Let, be three non-zero vectors such that is a unit vector perpendicular to both  If the angle between  is equal to

Detailed Solution for Vector Algebra: Scalar Triple Product(23 Nov) - Question 4


 = 

Vector Algebra: Scalar Triple Product(23 Nov) - Question 5

Let be non-coplanar unit vectors equally inclined to one another at an acute angle . Then  in terms of is equal to

Detailed Solution for Vector Algebra: Scalar Triple Product(23 Nov) - Question 5

 are unit vectors and equally inclined to each other at an acute angle θ.

∴ ABC is an equilateral triangle and

Vector Algebra: Scalar Triple Product(23 Nov) - Question 6

If  are two non-zero non-collinear vectors then  is equal to

Detailed Solution for Vector Algebra: Scalar Triple Product(23 Nov) - Question 6

Vector Algebra: Scalar Triple Product(23 Nov) - Question 7

Let and  is a unit vector such that , then  equals

Detailed Solution for Vector Algebra: Scalar Triple Product(23 Nov) - Question 7


or 2x + z = 0[ Using (ii)] or z = −2x From (i), (ii) and (iii), we have x+ x+ 4x= 1

Vector Algebra: Scalar Triple Product(23 Nov) - Question 8

If  for some non-zero vector , then the area of the triangle whose vertices are are non-coplanar)

Detailed Solution for Vector Algebra: Scalar Triple Product(23 Nov) - Question 8

Any vector can be represented in terms of three non-coplanar vectors 
Taking dot product with  respectively, we have 
From (i), we have

Vector Algebra: Scalar Triple Product(23 Nov) - Question 9

If  are three non-coplanar vectors, then the value of  is :

Detailed Solution for Vector Algebra: Scalar Triple Product(23 Nov) - Question 9

By definition of scalar triple product  can be written as

Vector Algebra: Scalar Triple Product(23 Nov) - Question 10

Let and be three non-coplanar vectors, and let and be the vectors defined by the relations and . Then the value of the expression  

Detailed Solution for Vector Algebra: Scalar Triple Product(23 Nov) - Question 10


Therefore, the given expression is equal to 1+0+1+0+1+0 = 3

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