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Vector Equation for Straight Line

9. Let vector...

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9. Let vector a = i + j and vector b = 2i - k , then point of intersection of the lines ra =ba and rb = ab is _________? r is arbitrary vector and i, j , k be unit orthonormal vectors.

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i, j, k

be unit orthonormal vectors and

a

be any vector, if

a \times r = j

a . r

Q. Assertion :If

i, j, k

are orthonormal unit vectors and

a

is any vector. If

a \times r = ˆ j,

a . r

is arbitrary constant. Reason: For any two arbitrary vectors

a

r

{| a \times r |}^{2} + {| a . r |}^{2} = {| a |}^{2} {| r |}^{2}

Q. (i) Find a unit vector perpendicular to both the vectors

4 \hat{i} - \hat{j} + 3 \hat{k} and - 2 \hat{i} + \hat{j} - 2 \hat{k} .

(ii) Find a unit vector perpendicular to the plane containing the vectors

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

Q. The position vectors of two points A and B are

i + j - k

2 i - j + k

respectively. Then

| A B | =

Q. For given vectors

\to a = 2 ˆ i - ˆ j + 2 ˆ k

b = - ˆ i + ˆ j - ˆ k

, then a unit vector in the direction of the vector

\to a + \to b

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Vector Equation for Straight Line

Standard XII Mathematics