A vector has magnitude same as that of and is parallel to . The and components of this vector in first quadrant are and 3 respectively where x

Question

A vector has magnitude same as that of $\vec{A} = 3 \hat{i} + 4 \hat{j}$ and is parallel to $\vec{B} = 4 \hat{i} + 3 \hat{j}$ . The $x$ and $y$ components of this vector in first quadrant are $x$ and 3 respectively where $x =$ _________ . [2024]

Smart Achievers · Accepted Answer

(4) Given $\vec{A} = 3 i + 4 j,$ $\vec{B} = 4 i + 3 j,$

$| A | = \sqrt{3^{2} + 4^{2}} = 5,$ $\hat{B} = \frac{4 i + 3 j}{5}, \frac{\vec{B}}{| B |} = \hat{B}$

Now, as per question, $\vec{C} = | A | \hat{B},$ mag of $\vec{A}$ and direction of B

$= (5) \frac{(4 i + 3 j)}{5} = 4 i + 3 j, 4 i + 3 j,$ $∴ x = 4$

Solution

Q.
A vector has magnitude same as that of $\vec{A} = 3 \hat{i} + 4 \hat{j}$ and is parallel to $\vec{B} = 4 \hat{i} + 3 \hat{j}$ . The $x$ and $y$ components of this vector in first quadrant are $x$ and 3 respectively where $x =$ _________ . [2024]

Want Us to Email you About Special Offers & Updates?

Solution

Q. A vector has magnitude same as that of A→=3i^+4j^ and is parallel to B→=4i^+3j^. The x and y components of this vector in first quadrant are x and 3 respectively where x= _________ . [2024]

Ans. (4) Given A→=3i+4j, B→=4i+3j, |A|=32+42=5, B^=4i+3j5,B→|B|=B^ Now, as per question, C→=|A|B^, mag of A→ and direction of B =(5)(4i+3j)5=4i+3j,4i+3j, ∴x=4

Want Us to Email you About Special Offers & Updates?

Q.
A vector has magnitude same as that of $\vec{A} = 3 \hat{i} + 4 \hat{j}$ and is parallel to $\vec{B} = 4 \hat{i} + 3 \hat{j}$ . The $x$ and $y$ components of this vector in first quadrant are $x$ and 3 respectively where $x =$ _________ . [2024]