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Find the direction cosines of a vector r ⃗ which is equally inclined with OX, OY and OZ. If....

Prove that [a ⃗, b ⃗, c ⃗+d ⃗ ]=[a ⃗, b ⃗, c ⃗ ]+[a ⃗, b ⃗, d ⃗ ]

Prove that [a ⃗+b ⃗, b ⃗+c ⃗, c ⃗+a ⃗ ]=2[a ⃗, b ⃗, c ⃗ ].

Show that the four points A, B, C and D with position vectors 4i ̂+5j ̂+k ̂, -(j ̂+k ̂ ), 3i ̂+9....

CONCEPT: EQUATION OF A LINE PASSING THROUGH TWO GIVEN POINTS

CONCEPT: SCALAR TRIPLE PRODUCT

Find λ if the vectors a ⃗=i ̂+3j ̂+k ̂, b ⃗=2i ̂-j ̂-k ̂ & c ⃗=λi ̂+7j ̂+3k ̂ are coplanar.

CONCEPT: EQUATION OF A LINE

Find a ⃗⋅(b ⃗×c ⃗ ), if a ⃗=2i ̂+j ̂+3k ̂, b ⃗=i ̂+2j ̂+k ̂ & c ⃗=3i ̂+j ̂+2k ̂.

COMPLETE EXERCISE 7.10 | ONE SHOT VIDEO

COMPLETE EXERCISE 7.9 | ONE SHOT VIDEO

COMPLETE EXERCISE 7.4 | ONE SHOT VIDEO

COMPLETE EXERCISE 7.3 | ONE SHOT VIDEO

COMPLETE EXERCISE 7.6 | ONE SHOT VIDEO

COMPLETE EXERCISE 7.2 | ONE SHOT VIDEO

COMPLETE EXERCISE 7.1 | ONE SHOT VIDEO

If A=[■(1&2&2@1&3&4@1&-1&3)], B=adj A, C=3A. Find |adj B|/|C| .

A body is launched from the ground & it follows a parabolic path given by y=ax^2+bx+c; a, b, c ∈ R..

If A=[■(3&2&1@4&-1&2@7&3&-3)], find A^(-1). Hence solve

Use the product [■(1&-1&2@0&2&-3@3&-2&4)][■(-2&0&1@9&2&-3@6&1&-2)] to solve:

Find (AB)^(-1) if A=[■(1&0@-4&2)] & B^(-1) [■(3&1@5&2)]

If A=[■(2&3&10@4&-6&5@6&9&-20)], find A^(-1). Using A^(-1) solve the system of equations: 2/x+3.....

If A=[■(2&-3&5@3&2&-4@1&1&-2)], find A^(-1). Hence solve the system of equations: 2x-3y+5-11....

If A is square matrix of order 3×3 such that |A|=2 then find |adj(adj A)|.