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Given two vectors vec(A)=3hat(i)+4hat(j)...

Given two vectors `vec(A)=3hat(i)+4hat(j)` and `vec(B)=hat(i)+hat(j).theta` is the angle between `vec(A)` and `vec(B)`. Which of the following statements is/are correct?

A

`|vecA|costheta((hati+hatj)/(sqrt(2)))` is the component of `vecA ` along `vecB` .

B

`|vecA|sintheta((hati-hatj)/(sqrt(2)))` is the component of `barA` perpendicular to `vecB`

C

`|vecA|costheta((hati-hatj)/(sqrt(2)))` is the component of `vecA` along `barB` .

D

`|vecA|sintheta((hati+hatj)/(sqrt(2)))` is the component of `vecA` perpendicular to `vecB` .

Text Solution

Verified by Experts

The correct Answer is:
A, B
Component of `vecA` along `vecB` is `|vecA| cos theta hatB` for `theta` being the angle between the vectors. Also `hatB= (hati+hatj)/(sqrt(2))` . So choice (a) is correct.
The vector `( hati-hatj)` is perpendicular to the vector `(hati+hatj)`
So the other resolved component is
`|vecA|sin theta= ((hati-hatj)/(sqrt(2)))`
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Knowledge Check

  • Give two vectors vec(A)==3hat(i)+4hat(j) and vec(B)=hat(i)+hat(j).theta is the angle between vec(A) and vec(B) . Which of the following statements is/are correct?

    A
    `|vec(A)|cos theta((hat(i)+hat(j))/(sqrt(2)))` is the component of `vec(A)` along `vec(B)`.
    B
    `|vec(A)|sin theta((hat(i)-hat(j))/sqrt(2))` is the component of `vec(A)` perpendicular to `vec(B)`.
    C
    `|vec(A)|cos theta((hat(i)-hat(j))/(sqrt(2)))` is the component of `vec(A)` along `vec(B)`.
    D
    `|vec(A)|sin theta((hat(i)+hat(j))/(sqrt(2)))` is the component of `vec(A)` perpendicular to `vec(B)`.

  • The angle between the two vector vec(A)= 5hat(i)+5hat(j) and vec(B)= 5hat(i)-5hat(j) will be

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    Zero
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    D
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    A
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    B
    `(3)/(sqrt2)`
    C
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    D
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