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Vector Algebra: Components of Vector(21 Nov) - JEE MCQ


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10 Questions MCQ Test Daily Test for JEE Preparation - Vector Algebra: Components of Vector(21 Nov)

Vector Algebra: Components of Vector(21 Nov) for JEE 2024 is part of Daily Test for JEE Preparation preparation. The Vector Algebra: Components of Vector(21 Nov) questions and answers have been prepared according to the JEE exam syllabus.The Vector Algebra: Components of Vector(21 Nov) MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Vector Algebra: Components of Vector(21 Nov) below.
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Vector Algebra: Components of Vector(21 Nov) - Question 1

The values of for which the vector  makes an obtuse angle with the z-axis and the vectors and  are mutually orthogonal are

Detailed Solution for Vector Algebra: Components of Vector(21 Nov) - Question 1


 or 3
if
for which if lies in the second quadrant
General value is

Vector Algebra: Components of Vector(21 Nov) - Question 2

If the and terms of a G.P. are positive numbers , and respectively, then find the angle between the vectors and 

Detailed Solution for Vector Algebra: Components of Vector(21 Nov) - Question 2

Let A be the first term and the common ratio of G.P.
So,
Similarly,
and

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Vector Algebra: Components of Vector(21 Nov) - Question 3

Let . If is a vector such that  and the angle between and is , then

Detailed Solution for Vector Algebra: Components of Vector(21 Nov) - Question 3


Squaring on both sides,

Vector Algebra: Components of Vector(21 Nov) - Question 4

If  and , then what is the value of

Detailed Solution for Vector Algebra: Components of Vector(21 Nov) - Question 4

As given,
is parallel to

Similarly, can be written as
where ∴ From equations (i) and (ii), we get and 

Vector Algebra: Components of Vector(21 Nov) - Question 5

Let  and . The vector which satisfies the equations and is given by

Detailed Solution for Vector Algebra: Components of Vector(21 Nov) - Question 5

Let Then

Vector Algebra: Components of Vector(21 Nov) - Question 6

What is the interior acute angle of the parallelogram whose sides are represented by the vectors and

Detailed Solution for Vector Algebra: Components of Vector(21 Nov) - Question 6

Vector Algebra: Components of Vector(21 Nov) - Question 7

If three vectors are such that and  and the angle between and is then  where  is equal to

Detailed Solution for Vector Algebra: Components of Vector(21 Nov) - Question 7

Given,
Since the vectors are non zero.
is parallel to . Let
Now

i.e.,

Vector Algebra: Components of Vector(21 Nov) - Question 8

For any vector , the value of  is

Detailed Solution for Vector Algebra: Components of Vector(21 Nov) - Question 8

Suppose


Similarly,

Vector Algebra: Components of Vector(21 Nov) - Question 9

Let A = (x + 4y) + (2x + y + 1)  and B = (y −2 x + 2) +(2x − 3y − 1)  where   and  are non-collinear vectors, if 3A = 2B then

Detailed Solution for Vector Algebra: Components of Vector(21 Nov) - Question 9

Given:


In question it is given,



and 
From the equation (1)

Vector Algebra: Components of Vector(21 Nov) - Question 10

What is a vector of unit length orthogonal to both the vectors and ?

Detailed Solution for Vector Algebra: Components of Vector(21 Nov) - Question 10


Vector of unit length orthogonal to both the vectors and 

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