If the vectors a - i -2 j -3 k - and b -3 i -6 j - mk - are collinear- then m -

Given: nbsp;a #8594;=i^ 2j^+3k^ #160;and #160;b #8594;=3i^ 6j^+mk^ nbsp;are collinear The #160;vectors #160;a #8594;=i^ 2j^+3k^ #160;and ...

128

You visited us 128 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Vector Triple Product

If the vector...

Question

If the vectors $\vec{a} = \hat{i} - 2 \hat{j} + 3 \hat{k} a n d \vec{b} = 3 \hat{i} - 6 \hat{j} + m \hat{k}$ are collinear, then m = ________________.

Open in App

Solution

Given: $\vec{a} = \hat{i} - 2 \hat{j} + 3 \hat{k} and \vec{b} = 3 \hat{i} - 6 \hat{j} + m \hat{k}$ are collinear

$The vectors \vec{a} = \hat{i} - 2 \hat{j} + 3 \hat{k} and \vec{b} = 3 \hat{i} - 6 \hat{j} + m \hat{k} are collinear \Rightarrow \frac{1}{3} = \frac{- 2}{- 6} = \frac{3}{m} \Rightarrow \frac{1}{3} = \frac{3}{m} \Rightarrow m = 9$

Hence, m = 9.

Suggest Corrections

Similar questions

Q. Show the each of the following triads of vectors are coplanar:
(i)

\vec{a} = \hat{i} + 2 \hat{j} - \hat{k}, \vec{b} = 3 \hat{i} + 2 \hat{j} + 7 \hat{k}, \vec{c} = 5 \hat{i} + 6 \hat{j} + 5 \hat{k}

(ii)

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

(iii)

\hat{a} = \hat{i} - 2 \hat{j} + 3 \hat{k}, \hat{b} = - 2 \hat{i} + 3 \hat{j} - 4 \hat{k}, \hat{c} = \hat{i} - 3 \hat{j} + 5 \hat{k}

Q. If the vectors 6i - 2j +3k , 2i +3j -6k and 3i + 6j -2k form a triangle, then it is

The position vectors of four [point A, B, C and D are $ˆ i + ˆ j + ˆ k, 2 ˆ i + 5 ˆ j, 3 ˆ i + 2 ˆ j - 3 ˆ k, ˆ i - 6 ˆ j - ˆ k$ then select the correct relation:

Q. lf a vector

¯ ¯¯ ¯ A = 2 ¯ i + 2 ¯ j + 3 ¯ ¯ ¯ k

and

¯ ¯¯ ¯ B = 3 ¯ i + 6 ¯ j + n ¯ ¯ ¯ k

, are perpendicular to each other, then the value of 'n' is:

Q. Find the cross products of the vectors
1.

a = i - 2 j + 3 k, b = 3 i - 6 j + 9 k

a = - 2 i - 4 k, b = i - 2 j - k, c = i - 4 j + 3 k

Join BYJU'S Learning Program

If the vectors a→=i^-2j^+3k^ and b→=3i^-6j^+mk^ are collinear, then m = ________________.

Given: a→=i^-2j^+3k^ and b→=3i^-6j^+mk^ are collinear The vectors a→=i^-2j^+3k^ and b→=3i^-6j^+mk^ are collinear⇒13=-2-6=3m⇒13=3m⇒m=9 ​Hence, m = 9.

If the vectors $\vec{a} = \hat{i} - 2 \hat{j} + 3 \hat{k} a n d \vec{b} = 3 \hat{i} - 6 \hat{j} + m \hat{k}$ are collinear, then m = ________________.