Let a - i -2 j - k - b - i - j - k and c - i - j - k- a vector in the plane a and b whose projection on c is 1-3 is-A- 3 i-j-3 kB- I - j -2 kC- 4 i - j -4 kD- 4 i - j -4 k

The correct option is C 4i j+4k verify from options. 4th option holds good ...

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Standard XII

Physics

Vectors

Let a = i +2 ...

Question

Let $\to a = i + 2 j + k, \to b = i - j + k a n d \to c = i + j - k,$ a vector in the plane $\to a a n d \to b$ whose projection on $\to c i s \frac{1}{\sqrt{3}} i s . . . . . . . .$

3i+j-3k

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4i+j-4k

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I+j-2k

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4i-j+4k

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Solution

The correct option is D
4i-j+4k

verify from options. 4^th option holds good

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Similar questions

Q. Let

a = i + 2 j + k, b = i - j + k

and

c = i + j - k

. A vector in the plane of

a

and

b

, whose projection on

c

\frac{1}{\sqrt{3}}

Q. Let

\to a = i + 2 j + k, \to b = i - j + k

and

\to c = i + j - k

, a vector in the plane

\to a

and

\to b

whose projection on

\to c

\frac{1}{\sqrt{3}}

is _____

Q. Find the angle between the vectors

\vec{a} and \vec{b}

, where
(i)

\vec{a} = \hat{i} - \hat{j} and \vec{b} = \hat{j} + \hat{k}

(ii)

\vec{a} = 3 \hat{i} - 2 \hat{j} - 6 \hat{k} and \vec{b} = 4 \hat{i} - \hat{j} + 8 \hat{k}

(iii)

\vec{a} = 2 \hat{i} - \hat{j} + 2 \hat{k} and \vec{b} = 4 \hat{i} + 4 \hat{j} - 2 \hat{k}

(iv)

\vec{a} = 2 \hat{i} - 3 \hat{j} + \hat{k} and \vec{b} = \hat{i} + \hat{j} - 2 \hat{k}

(v)

\vec{a} = \hat{i} + 2 \hat{j} - \hat{k}, \vec{b} = \hat{i} - \hat{j} + \hat{k}

Q. Find the volume of the parallelopiped whose coterminous edges are represented by the vectors:
(i)

\vec{a} = 2 \hat{i} + 3 \hat{j} + 4 \hat{k}, \vec{b} = \hat{i} + 2 \hat{j} - \hat{k}, \vec{c} = 3 \hat{i} - \hat{j} + 2 \hat{k}

(ii)

\vec{a} = 2 \hat{i} - 3 \hat{j} + 4 \hat{k}, \vec{b} = \hat{i} + 2 \hat{j} - \hat{k}, \vec{c} = 3 \hat{i} - \hat{j} - 2 \hat{k}

(iii)

\vec{a} = 11 \hat{i}, \vec{b} = 2 \hat{j}, \vec{c} = 13 \hat{k}

(iv)

\vec{a} = \hat{i} + \hat{j} + \hat{k}, \vec{b} = \hat{i} - \hat{j} + \hat{k}, \vec{c} = \hat{i} + 2 \hat{j} - \hat{k}

Let $\to a = i + 2 j + k, \to b = i - j + k a n d \to c = i + j - k,$ a vector in the plane $\to a a n d \to b$ whose projection on $\to c i s \frac{1}{\sqrt{3}} i s . . . . . . . .$

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Vectors

Standard XII Physics

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Let →a=i+2j+k,→b=i−j+k and →c=i+j−k, a vector in the plane →a and →b whose projection on →c is 1√3is........

The correct option is D 4i-j+4k verify from options. 4th option holds good

Let $\to a = i + 2 j + k, \to b = i - j + k a n d \to c = i + j - k,$ a vector in the plane $\to a a n d \to b$ whose projection on $\to c i s \frac{1}{\sqrt{3}} i s . . . . . . . .$

The correct option is D
4i-j+4k

verify from options. 4^th option holds good